(x-1)(7x+7)=89

Solution for (x-1)(7x+7)=89 equation:

(x-1)(7x+7)=89

We move all terms to the left:

(x-1)(7x+7)-(89)=0

We multiply parentheses ..

(+7x^2+7x-7x-7)-89=0

We get rid of parentheses

7x^2+7x-7x-7-89=0

We add all the numbers together, and all the variables

7x^2-96=0

a = 7; b = 0; c = -96;
Δ = b2-4ac
Δ = 02-4·7·(-96)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{42}}{2*7}=\frac{0-8\sqrt{42}}{14}
=-\frac{8\sqrt{42}}{14}
=-\frac{4\sqrt{42}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{42}}{2*7}=\frac{0+8\sqrt{42}}{14}
=\frac{8\sqrt{42}}{14}
=\frac{4\sqrt{42}}{7}
$