2X^2+10x-77=0

Solution for 2X^2+10x-77=0 equation:

2X^2+10X-77=0

a = 2; b = 10; c = -77;
Δ = b2-4ac
Δ = 102-4·2·(-77)
Δ = 716
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:

$\sqrt{\Delta}=\sqrt{716}=\sqrt{4*179}=\sqrt{4}*\sqrt{179}=2\sqrt{179}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{179}}{2*2}=\frac{-10-2\sqrt{179}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{179}}{2*2}=\frac{-10+2\sqrt{179}}{4}
$