10-4x^2+2=4x-8

Solution for 10-4x^2+2=4x-8 equation:

10-4x^2+2=4x-8

We move all terms to the left:

10-4x^2+2-(4x-8)=0

We add all the numbers together, and all the variables

-4x^2-(4x-8)+12=0

We get rid of parentheses

-4x^2-4x+8+12=0

We add all the numbers together, and all the variables

-4x^2-4x+20=0

a = -4; b = -4; c = +20;
Δ = b2-4ac
Δ = -42-4·(-4)·20
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{21}}{2*-4}=\frac{4-4\sqrt{21}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{21}}{2*-4}=\frac{4+4\sqrt{21}}{-8}
$