2x^2+24x-61=0

Solution for 2x^2+24x-61=0 equation:

2x^2+24x-61=0

a = 2; b = 24; c = -61;
Δ = b2-4ac
Δ = 242-4·2·(-61)
Δ = 1064
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:

$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{266}}{2*2}=\frac{-24-2\sqrt{266}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{266}}{2*2}=\frac{-24+2\sqrt{266}}{4}
$