7/8x-12=3/16x+5

Solution for 7/8x-12=3/16x+5 equation:

7/8x-12=3/16x+5

We move all terms to the left:

7/8x-12-(3/16x+5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 16x+5)!=0

x∈R


We get rid of parentheses

7/8x-3/16x-5-12=0

We calculate fractions


112x/128x^2+(-24x)/128x^2-5-12=0

We add all the numbers together, and all the variables

112x/128x^2+(-24x)/128x^2-17=0

We multiply all the terms by the denominator


112x+(-24x)-17*128x^2=0

Wy multiply elements

-2176x^2+112x+(-24x)=0

We get rid of parentheses

-2176x^2+112x-24x=0

We add all the numbers together, and all the variables

-2176x^2+88x=0

a = -2176; b = 88; c = 0;
Δ = b2-4ac
Δ = 882-4·(-2176)·0
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-88}{2*-2176}=\frac{-176}{-4352}
=11/272
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+88}{2*-2176}=\frac{0}{-4352}
=0
$