(84-x)(7x+61)=180

Solution for (84-x)(7x+61)=180 equation:

(84-x)(7x+61)=180

We move all terms to the left:

(84-x)(7x+61)-(180)=0

We add all the numbers together, and all the variables

(-1x+84)(7x+61)-180=0

We multiply parentheses ..

(-7x^2-61x+588x+5124)-180=0

We get rid of parentheses

-7x^2-61x+588x+5124-180=0

We add all the numbers together, and all the variables

-7x^2+527x+4944=0

a = -7; b = 527; c = +4944;
Δ = b2-4ac
Δ = 5272-4·(-7)·4944
Δ = 416161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(527)-\sqrt{416161}}{2*-7}=\frac{-527-\sqrt{416161}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(527)+\sqrt{416161}}{2*-7}=\frac{-527+\sqrt{416161}}{-14}
$