15-2x=7/8x

Solution for 15-2x=7/8x equation:

15-2x=7/8x

We move all terms to the left:

15-2x-(7/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2x-(+7/8x)+15=0

We get rid of parentheses

-2x-7/8x+15=0

We multiply all the terms by the denominator


-2x*8x+15*8x-7=0

Wy multiply elements

-16x^2+120x-7=0

a = -16; b = 120; c = -7;
Δ = b2-4ac
Δ = 1202-4·(-16)·(-7)
Δ = 13952
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:

$\sqrt{\Delta}=\sqrt{13952}=\sqrt{64*218}=\sqrt{64}*\sqrt{218}=8\sqrt{218}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-8\sqrt{218}}{2*-16}=\frac{-120-8\sqrt{218}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+8\sqrt{218}}{2*-16}=\frac{-120+8\sqrt{218}}{-32}
$