3x(x-6)=2x+1x-18

Solution for 3x(x-6)=2x+1x-18 equation:

3x(x-6)=2x+1x-18

We move all terms to the left:

3x(x-6)-(2x+1x-18)=0

We add all the numbers together, and all the variables

3x(x-6)-(3x-18)=0

We multiply parentheses

3x^2-18x-(3x-18)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-21x+18=0

a = 3; b = -21; c = +18;
Δ = b2-4ac
Δ = -212-4·3·18
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-15}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+15}{2*3}=\frac{36}{6}
=6
$