-5x^2+4=14x+12

Solution for -5x^2+4=14x+12 equation:

-5x^2+4=14x+12

We move all terms to the left:

-5x^2+4-(14x+12)=0

We get rid of parentheses

-5x^2-14x-12+4=0

We add all the numbers together, and all the variables

-5x^2-14x-8=0

a = -5; b = -14; c = -8;
Δ = b2-4ac
Δ = -142-4·(-5)·(-8)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*-5}=\frac{8}{-10}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*-5}=\frac{20}{-10}
=-2
$