(8x-20)=(1/2x+25)

Solution for (8x-20)=(1/2x+25) equation:

(8x-20)=(1/2x+25)

We move all terms to the left:

(8x-20)-((1/2x+25))=0


Domain of the equation: 2x+25))!=0

x∈R


We get rid of parentheses

8x-((1/2x+25))-20=0

We multiply all the terms by the denominator


8x*2x-20*2x+25))-((1+25))=0

We add all the numbers together, and all the variables

8x*2x-20*2x+25))-(26)=0

We add all the numbers together, and all the variables

8x*2x-20*2x=0

Wy multiply elements

16x^2-40x=0

a = 16; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·16·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*16}=\frac{80}{32}
=2+1/2
$