71/2-1/2x=33/4x+39

Solution for 71/2-1/2x=33/4x+39 equation:

71/2-1/2x=33/4x+39

We move all terms to the left:

71/2-1/2x-(33/4x+39)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+39)!=0

x∈R


We get rid of parentheses

-1/2x-33/4x-39+71/2=0

We calculate fractions


(-4x)/32x^2+(-264x)/32x^2+284x/32x^2-39=0

We multiply all the terms by the denominator


(-4x)+(-264x)+284x-39*32x^2=0

We add all the numbers together, and all the variables

284x+(-4x)+(-264x)-39*32x^2=0

Wy multiply elements

-1248x^2+284x+(-4x)+(-264x)=0

We get rid of parentheses

-1248x^2+284x-4x-264x=0

We add all the numbers together, and all the variables

-1248x^2+16x=0

a = -1248; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-1248)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-1248}=\frac{-32}{-2496}
=1/78
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-1248}=\frac{0}{-2496}
=0
$