8+31/2x=10+31/4x

Solution for 8+31/2x=10+31/4x equation:

8+31/2x=10+31/4x

We move all terms to the left:

8+31/2x-(10+31/4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

31/2x-(31/4x+10)+8=0

We get rid of parentheses

31/2x-31/4x-10+8=0

We calculate fractions


124x/8x^2+(-62x)/8x^2-10+8=0

We add all the numbers together, and all the variables

124x/8x^2+(-62x)/8x^2-2=0

We multiply all the terms by the denominator


124x+(-62x)-2*8x^2=0

Wy multiply elements

-16x^2+124x+(-62x)=0

We get rid of parentheses

-16x^2+124x-62x=0

We add all the numbers together, and all the variables

-16x^2+62x=0

a = -16; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·(-16)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*-16}=\frac{-124}{-32}
=3+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*-16}=\frac{0}{-32}
=0
$