(x-3)+2x(x-1)=x+7

Solution for (x-3)+2x(x-1)=x+7 equation:

(x-3)+2x(x-1)=x+7

We move all terms to the left:

(x-3)+2x(x-1)-(x+7)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-2x-10=0

a = 2; b = -2; c = -10;
Δ = b2-4ac
Δ = -22-4·2·(-10)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*2}=\frac{2-2\sqrt{21}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*2}=\frac{2+2\sqrt{21}}{4}
$