-5=8x^2+14x

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

-5=8x^2+14x

We move all terms to the left:

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

We get rid of parentheses

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

a = -8; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·(-8)·(-5)
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*-8}=\frac{8}{-16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*-8}=\frac{20}{-16}
=-1+1/4
$