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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+(2x-5)(x+7)=0

We multiply parentheses ..

(+2x^2+14x-5x-35)-1x=0

We get rid of parentheses

2x^2+14x-5x-1x-35=0

We add all the numbers together, and all the variables

2x^2+8x-35=0

a = 2; b = 8; c = -35;
Δ = b2-4ac
Δ = 82-4·2·(-35)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{86}}{2*2}=\frac{-8-2\sqrt{86}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{86}}{2*2}=\frac{-8+2\sqrt{86}}{4}
$