2x(3x+20)=45

Solution for 2x(3x+20)=45 equation:

2x(3x+20)=45

We move all terms to the left:

2x(3x+20)-(45)=0

We multiply parentheses

6x^2+40x-45=0

a = 6; b = 40; c = -45;
Δ = b2-4ac
Δ = 402-4·6·(-45)
Δ = 2680
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:

$\sqrt{\Delta}=\sqrt{2680}=\sqrt{4*670}=\sqrt{4}*\sqrt{670}=2\sqrt{670}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{670}}{2*6}=\frac{-40-2\sqrt{670}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{670}}{2*6}=\frac{-40+2\sqrt{670}}{12}
$