x(3x+4)=30

Solution for x(3x+4)=30 equation:

x(3x+4)=30

We move all terms to the left:

x(3x+4)-(30)=0

We multiply parentheses

3x^2+4x-30=0

a = 3; b = 4; c = -30;
Δ = b2-4ac
Δ = 42-4·3·(-30)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{94}}{2*3}=\frac{-4-2\sqrt{94}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{94}}{2*3}=\frac{-4+2\sqrt{94}}{6}
$