5x^2+192x-140=0

Solution for 5x^2+192x-140=0 equation:

5x^2+192x-140=0

a = 5; b = 192; c = -140;
Δ = b2-4ac
Δ = 1922-4·5·(-140)
Δ = 39664
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:

$\sqrt{\Delta}=\sqrt{39664}=\sqrt{16*2479}=\sqrt{16}*\sqrt{2479}=4\sqrt{2479}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-4\sqrt{2479}}{2*5}=\frac{-192-4\sqrt{2479}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+4\sqrt{2479}}{2*5}=\frac{-192+4\sqrt{2479}}{10}
$