1/2X-10=1/5x+16

Solution for 1/2X-10=1/5x+16 equation:

1/2X-10=1/5X+16

We move all terms to the left:

1/2X-10-(1/5X+16)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R



Domain of the equation: 5X+16)!=0

X∈R


We get rid of parentheses

1/2X-1/5X-16-10=0

We calculate fractions


5X/10X^2+(-2X)/10X^2-16-10=0

We add all the numbers together, and all the variables

5X/10X^2+(-2X)/10X^2-26=0

We multiply all the terms by the denominator


5X+(-2X)-26*10X^2=0

Wy multiply elements

-260X^2+5X+(-2X)=0

We get rid of parentheses

-260X^2+5X-2X=0

We add all the numbers together, and all the variables

-260X^2+3X=0

a = -260; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-260)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-260}=\frac{-6}{-520}
=3/260
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-260}=\frac{0}{-520}
=0
$