(3x-1)(x-5)+2=11x-55+2

Solution for (3x-1)(x-5)+2=11x-55+2 equation:

(3x-1)(x-5)+2=11x-55+2

We move all terms to the left:

(3x-1)(x-5)+2-(11x-55+2)=0

We add all the numbers together, and all the variables

(3x-1)(x-5)-(11x-53)+2=0

We get rid of parentheses

(3x-1)(x-5)-11x+53+2=0

We multiply parentheses ..

(+3x^2-15x-1x+5)-11x+53+2=0

We add all the numbers together, and all the variables

(+3x^2-15x-1x+5)-11x+55=0

We get rid of parentheses

3x^2-15x-1x-11x+5+55=0

We add all the numbers together, and all the variables

3x^2-27x+60=0

a = 3; b = -27; c = +60;
Δ = b2-4ac
Δ = -272-4·3·60
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3}{2*3}=\frac{24}{6}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3}{2*3}=\frac{30}{6}
=5
$