5/4x+8=1/2x+6

Solution for 5/4x+8=1/2x+6 equation:

5/4x+8=1/2x+6

We move all terms to the left:

5/4x+8-(1/2x+6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

5/4x-1/2x-6+8=0

We calculate fractions


10x/8x^2+(-4x)/8x^2-6+8=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2+10x+(-4x)=0

We get rid of parentheses

16x^2+10x-4x=0

We add all the numbers together, and all the variables

16x^2+6x=0

a = 16; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·16·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*16}=\frac{-12}{32}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*16}=\frac{0}{32}
=0
$