5x^2+45x=90

Solution for 5x^2+45x=90 equation:

5x^2+45x=90

We move all terms to the left:

5x^2+45x-(90)=0

a = 5; b = 45; c = -90;
Δ = b2-4ac
Δ = 452-4·5·(-90)
Δ = 3825
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:

$\sqrt{\Delta}=\sqrt{3825}=\sqrt{225*17}=\sqrt{225}*\sqrt{17}=15\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-15\sqrt{17}}{2*5}=\frac{-45-15\sqrt{17}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+15\sqrt{17}}{2*5}=\frac{-45+15\sqrt{17}}{10}
$