2+1/2x=-3/8x+16

Solution for 2+1/2x=-3/8x+16 equation:

2+1/2x=-3/8x+16

We move all terms to the left:

2+1/2x-(-3/8x+16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+16)!=0

x∈R


We get rid of parentheses

1/2x+3/8x-16+2=0

We calculate fractions


8x/16x^2+6x/16x^2-16+2=0

We add all the numbers together, and all the variables

8x/16x^2+6x/16x^2-14=0

We multiply all the terms by the denominator


8x+6x-14*16x^2=0

We add all the numbers together, and all the variables

14x-14*16x^2=0

Wy multiply elements

-224x^2+14x=0

a = -224; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-224)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-224}=\frac{-28}{-448}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-224}=\frac{0}{-448}
=0
$