3(x-2)(x-5)-2(x+9)(x-1)=18

Solution for 3(x-2)(x-5)-2(x+9)(x-1)=18 equation:

3(x-2)(x-5)-2(x+9)(x-1)=18

We move all terms to the left:

3(x-2)(x-5)-2(x+9)(x-1)-(18)=0

We multiply parentheses ..

3(+x^2-5x-2x+10)-2(x+9)(x-1)-18=0

We multiply parentheses

3x^2-15x-6x-2(x+9)(x-1)+30-18=0

We multiply parentheses ..

3x^2-2(+x^2-1x+9x-9)-15x-6x+30-18=0

We add all the numbers together, and all the variables

3x^2-2(+x^2-1x+9x-9)-21x+12=0

We multiply parentheses

3x^2-2x^2+2x-18x-21x+18+12=0

We add all the numbers together, and all the variables

x^2-37x+30=0

a = 1; b = -37; c = +30;
Δ = b2-4ac
Δ = -372-4·1·30
Δ = 1249
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{-(-37)-\sqrt{1249}}{2*1}=\frac{37-\sqrt{1249}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1249}}{2*1}=\frac{37+\sqrt{1249}}{2}
$