2+15x=7/8x

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

2+15x=7/8x

We move all terms to the left:

2+15x-(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

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

We get rid of parentheses

15x-7/8x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

120x^2+16x-7=0

a = 120; b = 16; c = -7;
Δ = b2-4ac
Δ = 162-4·120·(-7)
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{226}}{2*120}=\frac{-16-4\sqrt{226}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{226}}{2*120}=\frac{-16+4\sqrt{226}}{240}
$