(X2+2x-5)-(3x+2)=x1-1

Solution for (X2+2x-5)-(3x+2)=x1-1 equation:

(X2+2X-5)-(3X+2)=X1-1

We move all terms to the left:

(X2+2X-5)-(3X+2)-(X1-1)=0

We add all the numbers together, and all the variables

(+X^2+2X-5)-(3X+2)-(X-1)=0

We get rid of parentheses

X^2+2X-3X-X-5-2+1=0

We add all the numbers together, and all the variables

X^2-2X-6=0

a = 1; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·1·(-6)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*1}=\frac{2-2\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*1}=\frac{2+2\sqrt{7}}{2}
$