2X^2-5x-142=0

Solution for 2X^2-5x-142=0 equation:

2X^2-5X-142=0

a = 2; b = -5; c = -142;
Δ = b2-4ac
Δ = -52-4·2·(-142)
Δ = 1161
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:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{129}}{2*2}=\frac{5-3\sqrt{129}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{129}}{2*2}=\frac{5+3\sqrt{129}}{4}
$