(7x-6)(3x+17)=180

Solution for (7x-6)(3x+17)=180 equation:

(7x-6)(3x+17)=180

We move all terms to the left:

(7x-6)(3x+17)-(180)=0

We multiply parentheses ..

(+21x^2+119x-18x-102)-180=0

We get rid of parentheses

21x^2+119x-18x-102-180=0

We add all the numbers together, and all the variables

21x^2+101x-282=0

a = 21; b = 101; c = -282;
Δ = b2-4ac
Δ = 1012-4·21·(-282)
Δ = 33889
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{-(101)-\sqrt{33889}}{2*21}=\frac{-101-\sqrt{33889}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(101)+\sqrt{33889}}{2*21}=\frac{-101+\sqrt{33889}}{42}
$