.09x^2-5x-5000=0

Solution for .09x^2-5x-5000=0 equation:

.09x^2-5x-5000=0

a = .09; b = -5; c = -5000;
Δ = b2-4ac
Δ = -52-4·.09·(-5000)
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{73}}{2*.09}=\frac{5-5\sqrt{73}}{0.18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{73}}{2*.09}=\frac{5+5\sqrt{73}}{0.18}
$