31/2x+5=21/4x+6

Solution for 31/2x+5=21/4x+6 equation:

31/2x+5=21/4x+6

We move all terms to the left:

31/2x+5-(21/4x+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

31/2x-21/4x-6+5=0

We calculate fractions


124x/8x^2+(-42x)/8x^2-6+5=0

We add all the numbers together, and all the variables

124x/8x^2+(-42x)/8x^2-1=0

We multiply all the terms by the denominator


124x+(-42x)-1*8x^2=0

Wy multiply elements

-8x^2+124x+(-42x)=0

We get rid of parentheses

-8x^2+124x-42x=0

We add all the numbers together, and all the variables

-8x^2+82x=0

a = -8; b = 82; c = 0;
Δ = b2-4ac
Δ = 822-4·(-8)·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-82}{2*-8}=\frac{-164}{-16}
=10+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+82}{2*-8}=\frac{0}{-16}
=0
$