(x+1)(x+2)+4x-10=x+10x-1

Solution for (x+1)(x+2)+4x-10=x+10x-1 equation:

(x+1)(x+2)+4x-10=x+10x-1

We move all terms to the left:

(x+1)(x+2)+4x-10-(x+10x-1)=0

We add all the numbers together, and all the variables

(x+1)(x+2)+4x-(11x-1)-10=0

We add all the numbers together, and all the variables

4x+(x+1)(x+2)-(11x-1)-10=0

We get rid of parentheses

4x+(x+1)(x+2)-11x+1-10=0

We multiply parentheses ..

(+x^2+2x+x+2)+4x-11x+1-10=0

We add all the numbers together, and all the variables

(+x^2+2x+x+2)-7x-9=0

We get rid of parentheses

x^2+2x+x-7x+2-9=0

We add all the numbers together, and all the variables

x^2-4x-7=0

a = 1; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·1·(-7)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{11}}{2*1}=\frac{4-2\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{11}}{2*1}=\frac{4+2\sqrt{11}}{2}
$