(7x-7)(5x-3)=30

Solution for (7x-7)(5x-3)=30 equation:

(7x-7)(5x-3)=30

We move all terms to the left:

(7x-7)(5x-3)-(30)=0

We multiply parentheses ..

(+35x^2-21x-35x+21)-30=0

We get rid of parentheses

35x^2-21x-35x+21-30=0

We add all the numbers together, and all the variables

35x^2-56x-9=0

a = 35; b = -56; c = -9;
Δ = b2-4ac
Δ = -562-4·35·(-9)
Δ = 4396
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:

$\sqrt{\Delta}=\sqrt{4396}=\sqrt{4*1099}=\sqrt{4}*\sqrt{1099}=2\sqrt{1099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{1099}}{2*35}=\frac{56-2\sqrt{1099}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{1099}}{2*35}=\frac{56+2\sqrt{1099}}{70}
$