8x^2+18x=-20+32

Solution for 8x^2+18x=-20+32 equation:

8x^2+18x=-20+32

We move all terms to the left:

8x^2+18x-(-20+32)=0

We add all the numbers together, and all the variables

8x^2+18x-12=0

a = 8; b = 18; c = -12;
Δ = b2-4ac
Δ = 182-4·8·(-12)
Δ = 708
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{177}}{2*8}=\frac{-18-2\sqrt{177}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{177}}{2*8}=\frac{-18+2\sqrt{177}}{16}
$