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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+10x^2+35x-4x-14)-1x=0

We get rid of parentheses

10x^2+35x-4x-1x-14=0

We add all the numbers together, and all the variables

10x^2+30x-14=0

a = 10; b = 30; c = -14;
Δ = b2-4ac
Δ = 302-4·10·(-14)
Δ = 1460
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:

$\sqrt{\Delta}=\sqrt{1460}=\sqrt{4*365}=\sqrt{4}*\sqrt{365}=2\sqrt{365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{365}}{2*10}=\frac{-30-2\sqrt{365}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{365}}{2*10}=\frac{-30+2\sqrt{365}}{20}
$