15-8x2=6

Solution for 15-8x2=6 equation:

15-8x^2=6

We move all terms to the left:

15-8x^2-(6)=0

We add all the numbers together, and all the variables

-8x^2+9=0

a = -8; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-8)·9
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-8}=\frac{0-12\sqrt{2}}{-16}
=-\frac{12\sqrt{2}}{-16}
=-\frac{3\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-8}=\frac{0+12\sqrt{2}}{-16}
=\frac{12\sqrt{2}}{-16}
=\frac{3\sqrt{2}}{-4}
$