5x(x+6)=40

Solution for 5x(x+6)=40 equation:

5x(x+6)=40

We move all terms to the left:

5x(x+6)-(40)=0

We multiply parentheses

5x^2+30x-40=0

a = 5; b = 30; c = -40;
Δ = b2-4ac
Δ = 302-4·5·(-40)
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{17}}{2*5}=\frac{-30-10\sqrt{17}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{17}}{2*5}=\frac{-30+10\sqrt{17}}{10}
$