5x(x-3)=45

Solution for 5x(x-3)=45 equation:

5x(x-3)=45

We move all terms to the left:

5x(x-3)-(45)=0

We multiply parentheses

5x^2-15x-45=0

a = 5; b = -15; c = -45;
Δ = b2-4ac
Δ = -152-4·5·(-45)
Δ = 1125
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:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15\sqrt{5}}{2*5}=\frac{15-15\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15\sqrt{5}}{2*5}=\frac{15+15\sqrt{5}}{10}
$