2(7-x)=8-(2x^2-8x-7)

Solution for 2(7-x)=8-(2x^2-8x-7) equation:

2(7-x)=8-(2x^2-8x-7)

We move all terms to the left:

2(7-x)-(8-(2x^2-8x-7))=0

We add all the numbers together, and all the variables

2(-1x+7)-(8-(2x^2-8x-7))=0

We multiply parentheses

-2x-(8-(2x^2-8x-7))+14=0


We calculate terms in parentheses: -(8-(2x^2-8x-7)), so:

8-(2x^2-8x-7)

determiningTheFunctionDomain
-(2x^2-8x-7)+8

We get rid of parentheses

-2x^2+8x+7+8

We add all the numbers together, and all the variables

-2x^2+8x+15

Back to the equation:

-(-2x^2+8x+15)


We get rid of parentheses

2x^2-8x-2x-15+14=0

We add all the numbers together, and all the variables

2x^2-10x-1=0

a = 2; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·2·(-1)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{3}}{2*2}=\frac{10-6\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{3}}{2*2}=\frac{10+6\sqrt{3}}{4}
$