-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^2-52x=0

a = 96; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·96·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*96}=\frac{0}{192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*96}=\frac{104}{192}
=13/24
$