5(x-2)(x+1)=x+13

Solution for 5(x-2)(x+1)=x+13 equation:

5(x-2)(x+1)=x+13

We move all terms to the left:

5(x-2)(x+1)-(x+13)=0

We get rid of parentheses

5(x-2)(x+1)-x-13=0

We multiply parentheses ..

5(+x^2+x-2x-2)-x-13=0

We add all the numbers together, and all the variables

5(+x^2+x-2x-2)-1x-13=0

We multiply parentheses

5x^2+5x-10x-1x-10-13=0

We add all the numbers together, and all the variables

5x^2-6x-23=0

a = 5; b = -6; c = -23;
Δ = b2-4ac
Δ = -62-4·5·(-23)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{31}}{2*5}=\frac{6-4\sqrt{31}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{31}}{2*5}=\frac{6+4\sqrt{31}}{10}
$