7/8x+1=3/4x-2

Solution for 7/8x+1=3/4x-2 equation:

7/8x+1=3/4x-2

We move all terms to the left:

7/8x+1-(3/4x-2)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

7/8x-3/4x+2+1=0

We calculate fractions


28x/32x^2+(-24x)/32x^2+2+1=0

We add all the numbers together, and all the variables

28x/32x^2+(-24x)/32x^2+3=0

We multiply all the terms by the denominator


28x+(-24x)+3*32x^2=0

Wy multiply elements

96x^2+28x+(-24x)=0

We get rid of parentheses

96x^2+28x-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{-8}{192}
=-1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*96}=\frac{0}{192}
=0
$