3x(2x+1)=30

Solution for 3x(2x+1)=30 equation:

3x(2x+1)=30

We move all terms to the left:

3x(2x+1)-(30)=0

We multiply parentheses

6x^2+3x-30=0

a = 6; b = 3; c = -30;
Δ = b2-4ac
Δ = 32-4·6·(-30)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*6}=\frac{-30}{12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*6}=\frac{24}{12}
=2
$