(x-6)(2x-14)=3(8)

Solution for (x-6)(2x-14)=3(8) equation:

(x-6)(2x-14)=3(8)

We move all terms to the left:

(x-6)(2x-14)-(3(8))=0

determiningTheFunctionDomain
(x-6)(2x-14)-38=0

We multiply parentheses ..

(+2x^2-14x-12x+84)-38=0

We get rid of parentheses

2x^2-14x-12x+84-38=0

We add all the numbers together, and all the variables

2x^2-26x+46=0

a = 2; b = -26; c = +46;
Δ = b2-4ac
Δ = -262-4·2·46
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{77}}{2*2}=\frac{26-2\sqrt{77}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{77}}{2*2}=\frac{26+2\sqrt{77}}{4}
$