7/8x-1/4=5/16x+2

Solution for 7/8x-1/4=5/16x+2 equation:

7/8x-1/4=5/16x+2

We move all terms to the left:

7/8x-1/4-(5/16x+2)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 16x+2)!=0

x∈R


We get rid of parentheses

7/8x-5/16x-2-1/4=0

We calculate fractions


(-128x^2)/2048x^2+1792x/2048x^2+(-640x)/2048x^2-2=0

We multiply all the terms by the denominator


(-128x^2)+1792x+(-640x)-2*2048x^2=0

Wy multiply elements

(-128x^2)-4096x^2+1792x+(-640x)=0

We get rid of parentheses

-128x^2-4096x^2+1792x-640x=0

We add all the numbers together, and all the variables

-4224x^2+1152x=0

a = -4224; b = 1152; c = 0;
Δ = b2-4ac
Δ = 11522-4·(-4224)·0
Δ = 1327104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1327104}=1152$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1152)-1152}{2*-4224}=\frac{-2304}{-8448}
=3/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1152)+1152}{2*-4224}=\frac{0}{-8448}
=0
$