(137-2x)(5x)+25=180

Solution for (137-2x)(5x)+25=180 equation:

(137-2x)(5x)+25=180

We move all terms to the left:

(137-2x)(5x)+25-(180)=0

We add all the numbers together, and all the variables

(-2x+137)5x+25-180=0

We add all the numbers together, and all the variables

(-2x+137)5x-155=0

We multiply parentheses

-10x^2+685x-155=0

a = -10; b = 685; c = -155;
Δ = b2-4ac
Δ = 6852-4·(-10)·(-155)
Δ = 463025
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:

$\sqrt{\Delta}=\sqrt{463025}=\sqrt{25*18521}=\sqrt{25}*\sqrt{18521}=5\sqrt{18521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(685)-5\sqrt{18521}}{2*-10}=\frac{-685-5\sqrt{18521}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(685)+5\sqrt{18521}}{2*-10}=\frac{-685+5\sqrt{18521}}{-20}
$