12=5x^2+4x

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

12=5x^2+4x

We move all terms to the left:

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

We get rid of parentheses

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

a = -5; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-5)·12
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*-5}=\frac{-12}{-10}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*-5}=\frac{20}{-10}
=-2
$