5x^2=-16x-12

Solution for 5x^2=-16x-12 equation:

5x^2=-16x-12

We move all terms to the left:

5x^2-(-16x-12)=0

We get rid of parentheses

5x^2+16x+12=0

a = 5; b = 16; c = +12;
Δ = b2-4ac
Δ = 162-4·5·12
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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