5x^2-75x+180=0

Solution for 5x^2-75x+180=0 equation:

5x^2-75x+180=0

a = 5; b = -75; c = +180;
Δ = b2-4ac
Δ = -752-4·5·180
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-45}{2*5}=\frac{30}{10}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+45}{2*5}=\frac{120}{10}
=12
$