108x^2+64x-34=0

Solution for 108x^2+64x-34=0 equation:

108x^2+64x-34=0

a = 108; b = 64; c = -34;
Δ = b2-4ac
Δ = 642-4·108·(-34)
Δ = 18784
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:

$\sqrt{\Delta}=\sqrt{18784}=\sqrt{16*1174}=\sqrt{16}*\sqrt{1174}=4\sqrt{1174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{1174}}{2*108}=\frac{-64-4\sqrt{1174}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{1174}}{2*108}=\frac{-64+4\sqrt{1174}}{216}
$