2x(x-3)+3(x-1)=36

Solution for 2x(x-3)+3(x-1)=36 equation:

2x(x-3)+3(x-1)=36

We move all terms to the left:

2x(x-3)+3(x-1)-(36)=0

We multiply parentheses

2x^2-6x+3x-3-36=0

We add all the numbers together, and all the variables

2x^2-3x-39=0

a = 2; b = -3; c = -39;
Δ = b2-4ac
Δ = -32-4·2·(-39)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{321}}{2*2}=\frac{3-\sqrt{321}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{321}}{2*2}=\frac{3+\sqrt{321}}{4}
$