(x-3)(x+4)8=x

Solution for (x-3)(x+4)8=x equation:

(x-3)(x+4)8=x

We move all terms to the left:

(x-3)(x+4)8-(x)=0

We add all the numbers together, and all the variables

-1x+(x-3)(x+4)8=0

We multiply parentheses ..

(+x^2+4x-3x-12)8-1x=0

We multiply parentheses

8x^2+32x-24x-1x-96=0

We add all the numbers together, and all the variables

8x^2+7x-96=0

a = 8; b = 7; c = -96;
Δ = b2-4ac
Δ = 72-4·8·(-96)
Δ = 3121
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{-(7)-\sqrt{3121}}{2*8}=\frac{-7-\sqrt{3121}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{3121}}{2*8}=\frac{-7+\sqrt{3121}}{16}
$