5x(6+x)=45

Solution for 5x(6+x)=45 equation:

5x(6+x)=45

We move all terms to the left:

5x(6+x)-(45)=0

We add all the numbers together, and all the variables

5x(x+6)-45=0

We multiply parentheses

5x^2+30x-45=0

a = 5; b = 30; c = -45;
Δ = b2-4ac
Δ = 302-4·5·(-45)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{2}}{2*5}=\frac{-30-30\sqrt{2}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{2}}{2*5}=\frac{-30+30\sqrt{2}}{10}
$