x(2x-3)+3(x+x2)=45

Solution for x(2x-3)+3(x+x2)=45 equation:

x(2x-3)+3(x+x2)=45

We move all terms to the left:

x(2x-3)+3(x+x2)-(45)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

5x^2-45=0

a = 5; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·5·(-45)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*5}=\frac{30}{10}
=3
$