6-8x=12-5x^2

Solution for 6-8x=12-5x^2 equation:

6-8x=12-5x^2

We move all terms to the left:

6-8x-(12-5x^2)=0

We get rid of parentheses

5x^2-8x-12+6=0

We add all the numbers together, and all the variables

5x^2-8x-6=0

a = 5; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·5·(-6)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{46}}{2*5}=\frac{8-2\sqrt{46}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{46}}{2*5}=\frac{8+2\sqrt{46}}{10}
$