12^2=8^2+x^2-2*8*x*0.515

Solution for 12^2=8^2+x^2-2*8*x*0.515 equation:

12^2=8^2+x^2-2*8x*0.515

We move all terms to the left:

12^2-(8^2+x^2-2*8x*0.515)=0

We add all the numbers together, and all the variables

-(8^2+x^2-2*8x*0.515)+144=0

We get rid of parentheses

-x^2+2*8x*0.515+144-8^2=0

We add all the numbers together, and all the variables

-1x^2+2*8x*0.515+80=0

Wy multiply elements

-1x^2+8.24x+80=0

a = -1; b = 8.24; c = +80;
Δ = b2-4ac
Δ = 8.242-4·(-1)·80
Δ = 387.8976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8.24)-\sqrt{387.8976}}{2*-1}=\frac{-8.24-\sqrt{387.8976}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.24)+\sqrt{387.8976}}{2*-1}=\frac{-8.24+\sqrt{387.8976}}{-2}
$