(8x+7)(9x-4)=x

Solution for (8x+7)(9x-4)=x equation:

(8x+7)(9x-4)=x

We move all terms to the left:

(8x+7)(9x-4)-(x)=0

We add all the numbers together, and all the variables

-1x+(8x+7)(9x-4)=0

We multiply parentheses ..

(+72x^2-32x+63x-28)-1x=0

We get rid of parentheses

72x^2-32x+63x-1x-28=0

We add all the numbers together, and all the variables

72x^2+30x-28=0

a = 72; b = 30; c = -28;
Δ = b2-4ac
Δ = 302-4·72·(-28)
Δ = 8964
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:

$\sqrt{\Delta}=\sqrt{8964}=\sqrt{36*249}=\sqrt{36}*\sqrt{249}=6\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{249}}{2*72}=\frac{-30-6\sqrt{249}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{249}}{2*72}=\frac{-30+6\sqrt{249}}{144}
$