5x^2-6x-126=0

Solution for 5x^2-6x-126=0 equation:

5x^2-6x-126=0

a = 5; b = -6; c = -126;
Δ = b2-4ac
Δ = -62-4·5·(-126)
Δ = 2556
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:

$\sqrt{\Delta}=\sqrt{2556}=\sqrt{36*71}=\sqrt{36}*\sqrt{71}=6\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{71}}{2*5}=\frac{6-6\sqrt{71}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{71}}{2*5}=\frac{6+6\sqrt{71}}{10}
$