x(2x+3)-4(x-9)=x+45

Solution for x(2x+3)-4(x-9)=x+45 equation:

x(2x+3)-4(x-9)=x+45

We move all terms to the left:

x(2x+3)-4(x-9)-(x+45)=0

We multiply parentheses

2x^2+3x-4x-(x+45)+36=0

We get rid of parentheses

2x^2+3x-4x-x-45+36=0

We add all the numbers together, and all the variables

2x^2-2x-9=0

a = 2; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·2·(-9)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*2}=\frac{2-2\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*2}=\frac{2+2\sqrt{19}}{4}
$