3x^2-112x-128=0

Solution for 3x^2-112x-128=0 equation:

3x^2-112x-128=0

a = 3; b = -112; c = -128;
Δ = b2-4ac
Δ = -1122-4·3·(-128)
Δ = 14080
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:

$\sqrt{\Delta}=\sqrt{14080}=\sqrt{256*55}=\sqrt{256}*\sqrt{55}=16\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-16\sqrt{55}}{2*3}=\frac{112-16\sqrt{55}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+16\sqrt{55}}{2*3}=\frac{112+16\sqrt{55}}{6}
$