x^2-2x+1-5x-10=3x-7

Solution for x^2-2x+1-5x-10=3x-7 equation:

x^2-2x+1-5x-10=3x-7

We move all terms to the left:

x^2-2x+1-5x-10-(3x-7)=0

We add all the numbers together, and all the variables

x^2-7x-(3x-7)-9=0

We get rid of parentheses

x^2-7x-3x+7-9=0

We add all the numbers together, and all the variables

x^2-10x-2=0

a = 1; b = -10; c = -2;
Δ = b2-4ac
Δ = -102-4·1·(-2)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{3}}{2*1}=\frac{10-6\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{3}}{2*1}=\frac{10+6\sqrt{3}}{2}
$