(5x+1)(7x-23)=180

Solution for (5x+1)(7x-23)=180 equation:

(5x+1)(7x-23)=180

We move all terms to the left:

(5x+1)(7x-23)-(180)=0

We multiply parentheses ..

(+35x^2-115x+7x-23)-180=0

We get rid of parentheses

35x^2-115x+7x-23-180=0

We add all the numbers together, and all the variables

35x^2-108x-203=0

a = 35; b = -108; c = -203;
Δ = b2-4ac
Δ = -1082-4·35·(-203)
Δ = 40084
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:

$\sqrt{\Delta}=\sqrt{40084}=\sqrt{4*10021}=\sqrt{4}*\sqrt{10021}=2\sqrt{10021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{10021}}{2*35}=\frac{108-2\sqrt{10021}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{10021}}{2*35}=\frac{108+2\sqrt{10021}}{70}
$