(x-2)(3x-1)=288

Solution for (x-2)(3x-1)=288 equation:

(x-2)(3x-1)=288

We move all terms to the left:

(x-2)(3x-1)-(288)=0

We multiply parentheses ..

(+3x^2-1x-6x+2)-288=0

We get rid of parentheses

3x^2-1x-6x+2-288=0

We add all the numbers together, and all the variables

3x^2-7x-286=0

a = 3; b = -7; c = -286;
Δ = b2-4ac
Δ = -72-4·3·(-286)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-59}{2*3}=\frac{-52}{6}
=-8+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+59}{2*3}=\frac{66}{6}
=11
$