-10+2x=(1/2)(4x-8)

Solution for -10+2x=(1/2)(4x-8) equation:

-10+2x=(1/2)(4x-8)

We move all terms to the left:

-10+2x-((1/2)(4x-8))=0


Domain of the equation: 2)(4x-8))!=0

x∈R


We add all the numbers together, and all the variables

2x-((+1/2)(4x-8))-10=0

We multiply parentheses ..

-((+4x^2+1/2*-8))+2x-10=0

We multiply all the terms by the denominator


-((+4x^2+1+2x*2*-8))-10*2*-8))=0


We calculate terms in parentheses: -((+4x^2+1+2x*2*-8)), so:

(+4x^2+1+2x*2*-8)

We get rid of parentheses

4x^2+2x*2*+1-8

We add all the numbers together, and all the variables

4x^2+2x*2*-7

Wy multiply elements

4x^2+4x^2-7

We add all the numbers together, and all the variables

8x^2-7

Back to the equation:

-(8x^2-7)


We add all the numbers together, and all the variables

-(8x^2-7)=0

We get rid of parentheses

-8x^2+7=0

a = -8; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-8)·7
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*-8}=\frac{0-4\sqrt{14}}{-16}
=-\frac{4\sqrt{14}}{-16}
=-\frac{\sqrt{14}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*-8}=\frac{0+4\sqrt{14}}{-16}
=\frac{4\sqrt{14}}{-16}
=\frac{\sqrt{14}}{-4}
$