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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+3x^2+9x-5x-15)-1x=0

We get rid of parentheses

3x^2+9x-5x-1x-15=0

We add all the numbers together, and all the variables

3x^2+3x-15=0

a = 3; b = 3; c = -15;
Δ = b2-4ac
Δ = 32-4·3·(-15)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{21}}{2*3}=\frac{-3-3\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{21}}{2*3}=\frac{-3+3\sqrt{21}}{6}
$