(3x-7)*(x-5)=x

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+3x^2-15x-7x+35)-1x=0

We get rid of parentheses

3x^2-15x-7x-1x+35=0

We add all the numbers together, and all the variables

3x^2-23x+35=0

a = 3; b = -23; c = +35;
Δ = b2-4ac
Δ = -232-4·3·35
Δ = 109
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{-(-23)-\sqrt{109}}{2*3}=\frac{23-\sqrt{109}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{109}}{2*3}=\frac{23+\sqrt{109}}{6}
$