2x2-5x=x2+2x-1

Solution for 2x2-5x=x2+2x-1 equation:

2x^2-5x=x2+2x-1

We move all terms to the left:

2x^2-5x-(x2+2x-1)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-7x+1=0

a = 1; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·1·1
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{5}}{2*1}=\frac{7-3\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{5}}{2*1}=\frac{7+3\sqrt{5}}{2}
$