7/8x-1/2=3/26x+5

Solution for 7/8x-1/2=3/26x+5 equation:

7/8x-1/2=3/26x+5

We move all terms to the left:

7/8x-1/2-(3/26x+5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 26x+5)!=0

x∈R


We get rid of parentheses

7/8x-3/26x-5-1/2=0

We calculate fractions


(-416x^2)/832x^2+728x/832x^2+(-96x)/832x^2-5=0

We multiply all the terms by the denominator


(-416x^2)+728x+(-96x)-5*832x^2=0

Wy multiply elements

(-416x^2)-4160x^2+728x+(-96x)=0

We get rid of parentheses

-416x^2-4160x^2+728x-96x=0

We add all the numbers together, and all the variables

-4576x^2+632x=0

a = -4576; b = 632; c = 0;
Δ = b2-4ac
Δ = 6322-4·(-4576)·0
Δ = 399424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{399424}=632$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(632)-632}{2*-4576}=\frac{-1264}{-9152}
=79/572
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(632)+632}{2*-4576}=\frac{0}{-9152}
=0
$