(5x+7)(3x-1)=1

Solution for (5x+7)(3x-1)=1 equation:

(5x+7)(3x-1)=1

We move all terms to the left:

(5x+7)(3x-1)-(1)=0

We multiply parentheses ..

(+15x^2-5x+21x-7)-1=0

We get rid of parentheses

15x^2-5x+21x-7-1=0

We add all the numbers together, and all the variables

15x^2+16x-8=0

a = 15; b = 16; c = -8;
Δ = b2-4ac
Δ = 162-4·15·(-8)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{46}}{2*15}=\frac{-16-4\sqrt{46}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{46}}{2*15}=\frac{-16+4\sqrt{46}}{30}
$