5/8x+4=3/4x+7

Solution for 5/8x+4=3/4x+7 equation:

5/8x+4=3/4x+7

We move all terms to the left:

5/8x+4-(3/4x+7)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+7)!=0

x∈R


We get rid of parentheses

5/8x-3/4x-7+4=0

We calculate fractions


20x/32x^2+(-24x)/32x^2-7+4=0

We add all the numbers together, and all the variables

20x/32x^2+(-24x)/32x^2-3=0

We multiply all the terms by the denominator


20x+(-24x)-3*32x^2=0

Wy multiply elements

-96x^2+20x+(-24x)=0

We get rid of parentheses

-96x^2+20x-24x=0

We add all the numbers together, and all the variables

-96x^2-4x=0

a = -96; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-96)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-96}=\frac{8}{-192}
=-1/24
$