7/8x=15-2x

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

7/8x=15-2x

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7/8x+2x-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}
$