8x^2+14x=117

Solution for 8x^2+14x=117 equation:

8x^2+14x=117

We move all terms to the left:

8x^2+14x-(117)=0

a = 8; b = 14; c = -117;
Δ = b2-4ac
Δ = 142-4·8·(-117)
Δ = 3940
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:

$\sqrt{\Delta}=\sqrt{3940}=\sqrt{4*985}=\sqrt{4}*\sqrt{985}=2\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{985}}{2*8}=\frac{-14-2\sqrt{985}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{985}}{2*8}=\frac{-14+2\sqrt{985}}{16}
$