-8(2x-5)=-2(1/2x+10)

Solution for -8(2x-5)=-2(1/2x+10) equation:

-8(2x-5)=-2(1/2x+10)

We move all terms to the left:

-8(2x-5)-(-2(1/2x+10))=0


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

x∈R


We multiply parentheses

-16x-(-2(1/2x+10))+40=0

We multiply all the terms by the denominator


-16x*2x+40*2x+10))-(-2(1+10))=0

We add all the numbers together, and all the variables

-16x*2x+40*2x+10))-(-211)=0

We add all the numbers together, and all the variables

-16x*2x+40*2x=0

Wy multiply elements

-32x^2+80x=0

a = -32; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-32)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*-32}=\frac{-160}{-64}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-32}=\frac{0}{-64}
=0
$