If we know the quadratic formula, the quadratic formula is
x = [-b ± √(b²- 4ac)] / 2a
Gosh! So overwhelming! But let's look at the composition of a quadratic equation:
ax² + bx + c = 0
And we have 6x² - 3x = 1. So, what do we do? We need to put this quadratic equation into an easy form to find the value of a, b, and c to plug in to the equation.
We can just minus one on both sides to get this:
6x² - 3x - 1 = 0
Is it in the form of ax² + bx + c? Yes! a = 6, b = -3, and c = -1. Now, all we have to do is plug it into the quadratic formula.
x = [-b ± √(b²- 4ac)] / 2a
x = [-(-3) ± √((-3)²- 4(6)(-1))] / 2(6)
[3 ± √(9- 4(6)(-1))] / 12
[3 ± √(9 + 24)] / 12
[3 ± √(33)] / 12
At this point, we should just use a calculator, and recognize we have two answers because of the plus-or-minus sign! (or this sign: ±)
[3 ± √(33)] / 12
1) [3 + √(33)] / 12 = 0.73 approximately
2) [3 - √(33)] / 12 = -0.23 approximately
So, x=0.73 and x= -0.23.
