(5x-3)(6+x)=x

Solution for (5x-3)(6+x)=x equation:

(5x-3)(6+x)=x

We move all terms to the left:

(5x-3)(6+x)-(x)=0

We add all the numbers together, and all the variables

(5x-3)(x+6)-x=0

We add all the numbers together, and all the variables

-1x+(5x-3)(x+6)=0

We multiply parentheses ..

(+5x^2+30x-3x-18)-1x=0

We get rid of parentheses

5x^2+30x-3x-1x-18=0

We add all the numbers together, and all the variables

5x^2+26x-18=0

a = 5; b = 26; c = -18;
Δ = b2-4ac
Δ = 262-4·5·(-18)
Δ = 1036
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:

$\sqrt{\Delta}=\sqrt{1036}=\sqrt{4*259}=\sqrt{4}*\sqrt{259}=2\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{259}}{2*5}=\frac{-26-2\sqrt{259}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{259}}{2*5}=\frac{-26+2\sqrt{259}}{10}
$