5-1/2x=5/88x+2

Solution for 5-1/2x=5/88x+2 equation:

5-1/2x=5/88x+2

We move all terms to the left:

5-1/2x-(5/88x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 88x+2)!=0

x∈R


We get rid of parentheses

-1/2x-5/88x-2+5=0

We calculate fractions


(-88x)/176x^2+(-10x)/176x^2-2+5=0

We add all the numbers together, and all the variables

(-88x)/176x^2+(-10x)/176x^2+3=0

We multiply all the terms by the denominator


(-88x)+(-10x)+3*176x^2=0

Wy multiply elements

528x^2+(-88x)+(-10x)=0

We get rid of parentheses

528x^2-88x-10x=0

We add all the numbers together, and all the variables

528x^2-98x=0

a = 528; b = -98; c = 0;
Δ = b2-4ac
Δ = -982-4·528·0
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-98}{2*528}=\frac{0}{1056}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+98}{2*528}=\frac{196}{1056}
=49/264
$