5/2*x+6=7/4*x-8

Solution for 5/2*x+6=7/4*x-8 equation:

5/2x+6=7/4x-8

We move all terms to the left:

5/2x+6-(7/4x-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-8)!=0

x∈R


We get rid of parentheses

5/2x-7/4x+8+6=0

We calculate fractions


20x/8x^2+(-14x)/8x^2+8+6=0

We add all the numbers together, and all the variables

20x/8x^2+(-14x)/8x^2+14=0

We multiply all the terms by the denominator


20x+(-14x)+14*8x^2=0

Wy multiply elements

112x^2+20x+(-14x)=0

We get rid of parentheses

112x^2+20x-14x=0

We add all the numbers together, and all the variables

112x^2+6x=0

a = 112; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·112·0
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*112}=\frac{-12}{224}
=-3/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*112}=\frac{0}{224}
=0
$