(7x-8)(7x-8)=12

Solution for (7x-8)(7x-8)=12 equation:

(7x-8)(7x-8)=12

We move all terms to the left:

(7x-8)(7x-8)-(12)=0

We multiply parentheses ..

(+49x^2-56x-56x+64)-12=0

We get rid of parentheses

49x^2-56x-56x+64-12=0

We add all the numbers together, and all the variables

49x^2-112x+52=0

a = 49; b = -112; c = +52;
Δ = b2-4ac
Δ = -1122-4·49·52
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-28\sqrt{3}}{2*49}=\frac{112-28\sqrt{3}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+28\sqrt{3}}{2*49}=\frac{112+28\sqrt{3}}{98}
$