3x(x-30)+2x=540

Solution for 3x(x-30)+2x=540 equation:

3x(x-30)+2x=540

We move all terms to the left:

3x(x-30)+2x-(540)=0

We add all the numbers together, and all the variables

2x+3x(x-30)-540=0

We multiply parentheses

3x^2+2x-90x-540=0

We add all the numbers together, and all the variables

3x^2-88x-540=0

a = 3; b = -88; c = -540;
Δ = b2-4ac
Δ = -882-4·3·(-540)
Δ = 14224
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:

$\sqrt{\Delta}=\sqrt{14224}=\sqrt{16*889}=\sqrt{16}*\sqrt{889}=4\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{889}}{2*3}=\frac{88-4\sqrt{889}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{889}}{2*3}=\frac{88+4\sqrt{889}}{6}
$