71/2x-1/2x=15/4x+39

Solution for 71/2x-1/2x=15/4x+39 equation:

71/2x-1/2x=15/4x+39

We move all terms to the left:

71/2x-1/2x-(15/4x+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

71/2x-1/2x-15/4x-39=0

We calculate fractions


(-4x+71)/8x^2+(-30x)/8x^2-39=0

We multiply all the terms by the denominator


(-4x+71)+(-30x)-39*8x^2=0

Wy multiply elements

-312x^2+(-4x+71)+(-30x)=0

We get rid of parentheses

-312x^2-4x-30x+71=0

We add all the numbers together, and all the variables

-312x^2-34x+71=0

a = -312; b = -34; c = +71;
Δ = b2-4ac
Δ = -342-4·(-312)·71
Δ = 89764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{89764}=\sqrt{4*22441}=\sqrt{4}*\sqrt{22441}=2\sqrt{22441}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{22441}}{2*-312}=\frac{34-2\sqrt{22441}}{-624}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{22441}}{2*-312}=\frac{34+2\sqrt{22441}}{-624}
$