7x(8x-4)=91+7x

Solution for 7x(8x-4)=91+7x equation:

7x(8x-4)=91+7x

We move all terms to the left:

7x(8x-4)-(91+7x)=0

We add all the numbers together, and all the variables

7x(8x-4)-(7x+91)=0

We multiply parentheses

56x^2-28x-(7x+91)=0

We get rid of parentheses

56x^2-28x-7x-91=0

We add all the numbers together, and all the variables

56x^2-35x-91=0

a = 56; b = -35; c = -91;
Δ = b2-4ac
Δ = -352-4·56·(-91)
Δ = 21609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21609}=147$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-147}{2*56}=\frac{-112}{112}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+147}{2*56}=\frac{182}{112}
=1+5/8
$