1/4x-3=-5/2x+8

Solution for 1/4x-3=-5/2x+8 equation:

1/4x-3=-5/2x+8

We move all terms to the left:

1/4x-3-(-5/2x+8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+8)!=0

x∈R


We get rid of parentheses

1/4x+5/2x-8-3=0

We calculate fractions


2x/8x^2+20x/8x^2-8-3=0

We add all the numbers together, and all the variables

2x/8x^2+20x/8x^2-11=0

We multiply all the terms by the denominator


2x+20x-11*8x^2=0

We add all the numbers together, and all the variables

22x-11*8x^2=0

Wy multiply elements

-88x^2+22x=0

a = -88; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-88)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-88}=\frac{-44}{-176}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-88}=\frac{0}{-176}
=0
$