45x^2+50x-4500=0

Solution for 45x^2+50x-4500=0 equation:

45x^2+50x-4500=0

a = 45; b = 50; c = -4500;
Δ = b2-4ac
Δ = 502-4·45·(-4500)
Δ = 812500
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:

$\sqrt{\Delta}=\sqrt{812500}=\sqrt{62500*13}=\sqrt{62500}*\sqrt{13}=250\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-250\sqrt{13}}{2*45}=\frac{-50-250\sqrt{13}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+250\sqrt{13}}{2*45}=\frac{-50+250\sqrt{13}}{90}
$