780=8+x(2x-6)

Solution for 780=8+x(2x-6) equation:

780=8+x(2x-6)

We move all terms to the left:

780-(8+x(2x-6))=0


We calculate terms in parentheses: -(8+x(2x-6)), so:

8+x(2x-6)

determiningTheFunctionDomain
x(2x-6)+8

We multiply parentheses

2x^2-6x+8

Back to the equation:

-(2x^2-6x+8)


We get rid of parentheses

-2x^2+6x-8+780=0

We add all the numbers together, and all the variables

-2x^2+6x+772=0

a = -2; b = 6; c = +772;
Δ = b2-4ac
Δ = 62-4·(-2)·772
Δ = 6212
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:

$\sqrt{\Delta}=\sqrt{6212}=\sqrt{4*1553}=\sqrt{4}*\sqrt{1553}=2\sqrt{1553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1553}}{2*-2}=\frac{-6-2\sqrt{1553}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1553}}{2*-2}=\frac{-6+2\sqrt{1553}}{-4}
$