31/2x-3/4x=16

Solution for 31/2x-3/4x=16 equation:

31/2x-3/4x=16

We move all terms to the left:

31/2x-3/4x-(16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


124x/8x^2+(-6x)/8x^2-16=0

We multiply all the terms by the denominator


124x+(-6x)-16*8x^2=0

Wy multiply elements

-128x^2+124x+(-6x)=0

We get rid of parentheses

-128x^2+124x-6x=0

We add all the numbers together, and all the variables

-128x^2+118x=0

a = -128; b = 118; c = 0;
Δ = b2-4ac
Δ = 1182-4·(-128)·0
Δ = 13924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13924}=118$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(118)-118}{2*-128}=\frac{-236}{-256}
=59/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(118)+118}{2*-128}=\frac{0}{-256}
=0
$