8x^2-80=-24x

Solution for 8x^2-80=-24x equation:

8x^2-80=-24x

We move all terms to the left:

8x^2-80-(-24x)=0

We get rid of parentheses

8x^2+24x-80=0

a = 8; b = 24; c = -80;
Δ = b2-4ac
Δ = 242-4·8·(-80)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-56}{2*8}=\frac{-80}{16}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+56}{2*8}=\frac{32}{16}
=2
$