(13x-1)(7x-5)=134

Solution for (13x-1)(7x-5)=134 equation:

(13x-1)(7x-5)=134

We move all terms to the left:

(13x-1)(7x-5)-(134)=0

We multiply parentheses ..

(+91x^2-65x-7x+5)-134=0

We get rid of parentheses

91x^2-65x-7x+5-134=0

We add all the numbers together, and all the variables

91x^2-72x-129=0

a = 91; b = -72; c = -129;
Δ = b2-4ac
Δ = -722-4·91·(-129)
Δ = 52140
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:

$\sqrt{\Delta}=\sqrt{52140}=\sqrt{4*13035}=\sqrt{4}*\sqrt{13035}=2\sqrt{13035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{13035}}{2*91}=\frac{72-2\sqrt{13035}}{182}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{13035}}{2*91}=\frac{72+2\sqrt{13035}}{182}
$