12x^2+52x-25=0

Solution for 12x^2+52x-25=0 equation:

12x^2+52x-25=0

a = 12; b = 52; c = -25;
Δ = b2-4ac
Δ = 522-4·12·(-25)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-8\sqrt{61}}{2*12}=\frac{-52-8\sqrt{61}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+8\sqrt{61}}{2*12}=\frac{-52+8\sqrt{61}}{24}
$