8x^2=12x+216

Solution for 8x^2=12x+216 equation:

8x^2=12x+216

We move all terms to the left:

8x^2-(12x+216)=0

We get rid of parentheses

8x^2-12x-216=0

a = 8; b = -12; c = -216;
Δ = b2-4ac
Δ = -122-4·8·(-216)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-84}{2*8}=\frac{-72}{16}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+84}{2*8}=\frac{96}{16}
=6
$