12x^2-76x-78=0

Solution for 12x^2-76x-78=0 equation:

12x^2-76x-78=0

a = 12; b = -76; c = -78;
Δ = b2-4ac
Δ = -762-4·12·(-78)
Δ = 9520
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:

$\sqrt{\Delta}=\sqrt{9520}=\sqrt{16*595}=\sqrt{16}*\sqrt{595}=4\sqrt{595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{595}}{2*12}=\frac{76-4\sqrt{595}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{595}}{2*12}=\frac{76+4\sqrt{595}}{24}
$