12x^2-176x-105=0

Solution for 12x^2-176x-105=0 equation:

12x^2-176x-105=0

a = 12; b = -176; c = -105;
Δ = b2-4ac
Δ = -1762-4·12·(-105)
Δ = 36016
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:

$\sqrt{\Delta}=\sqrt{36016}=\sqrt{16*2251}=\sqrt{16}*\sqrt{2251}=4\sqrt{2251}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-4\sqrt{2251}}{2*12}=\frac{176-4\sqrt{2251}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+4\sqrt{2251}}{2*12}=\frac{176+4\sqrt{2251}}{24}
$