(3x+7)(-2x+5)=x

Solution for (3x+7)(-2x+5)=x equation:

(3x+7)(-2x+5)=x

We move all terms to the left:

(3x+7)(-2x+5)-(x)=0

We add all the numbers together, and all the variables

-1x+(3x+7)(-2x+5)=0

We multiply parentheses ..

(-6x^2+15x-14x+35)-1x=0

We get rid of parentheses

-6x^2+15x-14x-1x+35=0

We add all the numbers together, and all the variables

-6x^2+35=0

a = -6; b = 0; c = +35;
Δ = b2-4ac
Δ = 02-4·(-6)·35
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*-6}=\frac{0-2\sqrt{210}}{-12}
=-\frac{2\sqrt{210}}{-12}
=-\frac{\sqrt{210}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*-6}=\frac{0+2\sqrt{210}}{-12}
=\frac{2\sqrt{210}}{-12}
=\frac{\sqrt{210}}{-6}
$