5x-5=(1/2)(10x-10)

Solution for 5x-5=(1/2)(10x-10) equation:

5x-5=(1/2)(10x-10)

We move all terms to the left:

5x-5-((1/2)(10x-10))=0


Domain of the equation: 2)(10x-10))!=0

x∈R


We add all the numbers together, and all the variables

5x-((+1/2)(10x-10))-5=0

We multiply parentheses ..

-((+10x^2+1/2*-10))+5x-5=0

We multiply all the terms by the denominator


-((+10x^2+1+5x*2*-10))-5*2*-10))=0


We calculate terms in parentheses: -((+10x^2+1+5x*2*-10)), so:

(+10x^2+1+5x*2*-10)

We get rid of parentheses

10x^2+5x*2*+1-10

We add all the numbers together, and all the variables

10x^2+5x*2*-9

Wy multiply elements

10x^2+10x^2-9

We add all the numbers together, and all the variables

20x^2-9

Back to the equation:

-(20x^2-9)


We add all the numbers together, and all the variables

-(20x^2-9)=0

We get rid of parentheses

-20x^2+9=0

a = -20; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-20)·9
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*-20}=\frac{0-12\sqrt{5}}{-40}
=-\frac{12\sqrt{5}}{-40}
=-\frac{3\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*-20}=\frac{0+12\sqrt{5}}{-40}
=\frac{12\sqrt{5}}{-40}
=\frac{3\sqrt{5}}{-10}
$