(x+1)(5x-1)-(x+1)(3x-12)=0

Solution for (x+1)(5x-1)-(x+1)(3x-12)=0 equation:

(x+1)(5x-1)-(x+1)(3x-12)=0

We multiply parentheses ..

(+5x^2-1x+5x-1)-(x+1)(3x-12)=0

We get rid of parentheses

5x^2-1x+5x-(x+1)(3x-12)-1=0

We multiply parentheses ..

5x^2-(+3x^2-12x+3x-12)-1x+5x-1=0

We add all the numbers together, and all the variables

5x^2-(+3x^2-12x+3x-12)+4x-1=0

We get rid of parentheses

5x^2-3x^2+12x-3x+4x+12-1=0

We add all the numbers together, and all the variables

2x^2+13x+11=0

a = 2; b = 13; c = +11;
Δ = b2-4ac
Δ = 132-4·2·11
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-9}{2*2}=\frac{-22}{4}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+9}{2*2}=\frac{-4}{4}
=-1
$