2x^2-76x+140=0

Solution for 2x^2-76x+140=0 equation:

2x^2-76x+140=0

a = 2; b = -76; c = +140;
Δ = b2-4ac
Δ = -762-4·2·140
Δ = 4656
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:

$\sqrt{\Delta}=\sqrt{4656}=\sqrt{16*291}=\sqrt{16}*\sqrt{291}=4\sqrt{291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{291}}{2*2}=\frac{76-4\sqrt{291}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{291}}{2*2}=\frac{76+4\sqrt{291}}{4}
$