(7x-1)(8x-14)=90

Solution for (7x-1)(8x-14)=90 equation:

(7x-1)(8x-14)=90

We move all terms to the left:

(7x-1)(8x-14)-(90)=0

We multiply parentheses ..

(+56x^2-98x-8x+14)-90=0

We get rid of parentheses

56x^2-98x-8x+14-90=0

We add all the numbers together, and all the variables

56x^2-106x-76=0

a = 56; b = -106; c = -76;
Δ = b2-4ac
Δ = -1062-4·56·(-76)
Δ = 28260
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:

$\sqrt{\Delta}=\sqrt{28260}=\sqrt{36*785}=\sqrt{36}*\sqrt{785}=6\sqrt{785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-6\sqrt{785}}{2*56}=\frac{106-6\sqrt{785}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+6\sqrt{785}}{2*56}=\frac{106+6\sqrt{785}}{112}
$