12x^2-175x-2700=0

Solution for 12x^2-175x-2700=0 equation:

12x^2-175x-2700=0

a = 12; b = -175; c = -2700;
Δ = b2-4ac
Δ = -1752-4·12·(-2700)
Δ = 160225
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:

$\sqrt{\Delta}=\sqrt{160225}=\sqrt{25*6409}=\sqrt{25}*\sqrt{6409}=5\sqrt{6409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-175)-5\sqrt{6409}}{2*12}=\frac{175-5\sqrt{6409}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-175)+5\sqrt{6409}}{2*12}=\frac{175+5\sqrt{6409}}{24}
$