2X^2-8x-61=0

Solution for 2X^2-8x-61=0 equation:

2X^2-8X-61=0

a = 2; b = -8; c = -61;
Δ = b2-4ac
Δ = -82-4·2·(-61)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{138}}{2*2}=\frac{8-2\sqrt{138}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{138}}{2*2}=\frac{8+2\sqrt{138}}{4}
$