2x(x-5)=x-7

Solution for 2x(x-5)=x-7 equation:

2x(x-5)=x-7

We move all terms to the left:

2x(x-5)-(x-7)=0

We multiply parentheses

2x^2-10x-(x-7)=0

We get rid of parentheses

2x^2-10x-x+7=0

We add all the numbers together, and all the variables

2x^2-11x+7=0

a = 2; b = -11; c = +7;
Δ = b2-4ac
Δ = -112-4·2·7
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{65}}{2*2}=\frac{11-\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{65}}{2*2}=\frac{11+\sqrt{65}}{4}
$