-5x^2+4=12x+8

Solution for -5x^2+4=12x+8 equation:

-5x^2+4=12x+8

We move all terms to the left:

-5x^2+4-(12x+8)=0

We get rid of parentheses

-5x^2-12x-8+4=0

We add all the numbers together, and all the variables

-5x^2-12x-4=0

a = -5; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·(-5)·(-4)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8}{2*-5}=\frac{4}{-10}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8}{2*-5}=\frac{20}{-10}
=-2
$