4x^2+38x-108=0

Solution for 4x^2+38x-108=0 equation:

4x^2+38x-108=0

a = 4; b = 38; c = -108;
Δ = b2-4ac
Δ = 382-4·4·(-108)
Δ = 3172
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:

$\sqrt{\Delta}=\sqrt{3172}=\sqrt{4*793}=\sqrt{4}*\sqrt{793}=2\sqrt{793}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{793}}{2*4}=\frac{-38-2\sqrt{793}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{793}}{2*4}=\frac{-38+2\sqrt{793}}{8}
$