5x2+124x-45=0

Solution for 5x2+124x-45=0 equation:

5x^2+124x-45=0

a = 5; b = 124; c = -45;
Δ = b2-4ac
Δ = 1242-4·5·(-45)
Δ = 16276
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:

$\sqrt{\Delta}=\sqrt{16276}=\sqrt{4*4069}=\sqrt{4}*\sqrt{4069}=2\sqrt{4069}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-2\sqrt{4069}}{2*5}=\frac{-124-2\sqrt{4069}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+2\sqrt{4069}}{2*5}=\frac{-124+2\sqrt{4069}}{10}
$