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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+2x^2-14x-5x+35)-2x=0

We get rid of parentheses

2x^2-14x-5x-2x+35=0

We add all the numbers together, and all the variables

2x^2-21x+35=0

a = 2; b = -21; c = +35;
Δ = b2-4ac
Δ = -212-4·2·35
Δ = 161
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{-(-21)-\sqrt{161}}{2*2}=\frac{21-\sqrt{161}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{161}}{2*2}=\frac{21+\sqrt{161}}{4}
$