20+31/2x=30+23/4x

Solution for 20+31/2x=30+23/4x equation:

20+31/2x=30+23/4x

We move all terms to the left:

20+31/2x-(30+23/4x)=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-(23/4x+30)+20=0

We get rid of parentheses

31/2x-23/4x-30+20=0

We calculate fractions


124x/8x^2+(-46x)/8x^2-30+20=0

We add all the numbers together, and all the variables

124x/8x^2+(-46x)/8x^2-10=0

We multiply all the terms by the denominator


124x+(-46x)-10*8x^2=0

Wy multiply elements

-80x^2+124x+(-46x)=0

We get rid of parentheses

-80x^2+124x-46x=0

We add all the numbers together, and all the variables

-80x^2+78x=0

a = -80; b = 78; c = 0;
Δ = b2-4ac
Δ = 782-4·(-80)·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-78}{2*-80}=\frac{-156}{-160}
=39/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+78}{2*-80}=\frac{0}{-160}
=0
$