2x^2-15x-126=0

Solution for 2x^2-15x-126=0 equation:

2x^2-15x-126=0

a = 2; b = -15; c = -126;
Δ = b2-4ac
Δ = -152-4·2·(-126)
Δ = 1233
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:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{137}}{2*2}=\frac{15-3\sqrt{137}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{137}}{2*2}=\frac{15+3\sqrt{137}}{4}
$