2x(x-45)+(x-45)+(x-45)=540

Solution for 2x(x-45)+(x-45)+(x-45)=540 equation:

2x(x-45)+(x-45)+(x-45)=540

We move all terms to the left:

2x(x-45)+(x-45)+(x-45)-(540)=0

We multiply parentheses

2x^2-90x+(x-45)+(x-45)-540=0

We get rid of parentheses

2x^2-90x+x+x-45-45-540=0

We add all the numbers together, and all the variables

2x^2-88x-630=0

a = 2; b = -88; c = -630;
Δ = b2-4ac
Δ = -882-4·2·(-630)
Δ = 12784
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:

$\sqrt{\Delta}=\sqrt{12784}=\sqrt{16*799}=\sqrt{16}*\sqrt{799}=4\sqrt{799}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{799}}{2*2}=\frac{88-4\sqrt{799}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{799}}{2*2}=\frac{88+4\sqrt{799}}{4}
$