5x(x+30)=45

Solution for 5x(x+30)=45 equation:

5x(x+30)=45

We move all terms to the left:

5x(x+30)-(45)=0

We multiply parentheses

5x^2+150x-45=0

a = 5; b = 150; c = -45;
Δ = b2-4ac
Δ = 1502-4·5·(-45)
Δ = 23400
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:

$\sqrt{\Delta}=\sqrt{23400}=\sqrt{900*26}=\sqrt{900}*\sqrt{26}=30\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-30\sqrt{26}}{2*5}=\frac{-150-30\sqrt{26}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+30\sqrt{26}}{2*5}=\frac{-150+30\sqrt{26}}{10}
$