20=(6x-1)(x-14)=180

Solution for 20=(6x-1)(x-14)=180 equation:

20=(6x-1)(x-14)=180

We move all terms to the left:

20-((6x-1)(x-14))=0

We multiply parentheses ..

-((+6x^2-84x-1x+14))+20=0


We calculate terms in parentheses: -((+6x^2-84x-1x+14)), so:

(+6x^2-84x-1x+14)

We get rid of parentheses

6x^2-84x-1x+14

We add all the numbers together, and all the variables

6x^2-85x+14

Back to the equation:

-(6x^2-85x+14)


We get rid of parentheses

-6x^2+85x-14+20=0

We add all the numbers together, and all the variables

-6x^2+85x+6=0

a = -6; b = 85; c = +6;
Δ = b2-4ac
Δ = 852-4·(-6)·6
Δ = 7369
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{-(85)-\sqrt{7369}}{2*-6}=\frac{-85-\sqrt{7369}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+\sqrt{7369}}{2*-6}=\frac{-85+\sqrt{7369}}{-12}
$