5x^2+8=-14x

Solution for 5x^2+8=-14x equation:

5x^2+8=-14x

We move all terms to the left:

5x^2+8-(-14x)=0

We get rid of parentheses

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