5a^2-75a+90=0

Solution for 5a^2-75a+90=0 equation:

5a^2-75a+90=0

a = 5; b = -75; c = +90;
Δ = b2-4ac
Δ = -752-4·5·90
Δ = 3825
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3825}=\sqrt{225*17}=\sqrt{225}*\sqrt{17}=15\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-15\sqrt{17}}{2*5}=\frac{75-15\sqrt{17}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+15\sqrt{17}}{2*5}=\frac{75+15\sqrt{17}}{10}
$