5/2X=16-7x

Solution for 5/2X=16-7x equation:

5/2X=16-7X

We move all terms to the left:

5/2X-(16-7X)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

5/2X-(-7X+16)=0

We get rid of parentheses

5/2X+7X-16=0

We multiply all the terms by the denominator


7X*2X-16*2X+5=0

Wy multiply elements

14X^2-32X+5=0

a = 14; b = -32; c = +5;
Δ = b2-4ac
Δ = -322-4·14·5
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{186}}{2*14}=\frac{32-2\sqrt{186}}{28}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{186}}{2*14}=\frac{32+2\sqrt{186}}{28}
$