x(30x+30)=40

Solution for x(30x+30)=40 equation:

x(30x+30)=40

We move all terms to the left:

x(30x+30)-(40)=0

We multiply parentheses

30x^2+30x-40=0

a = 30; b = 30; c = -40;
Δ = b2-4ac
Δ = 302-4·30·(-40)
Δ = 5700
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:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{57}}{2*30}=\frac{-30-10\sqrt{57}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{57}}{2*30}=\frac{-30+10\sqrt{57}}{60}
$