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

-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 = 14848
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:

$\sqrt{\Delta}=\sqrt{14848}=\sqrt{256*58}=\sqrt{256}*\sqrt{58}=16\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-16\sqrt{58}}{2*-16}=\frac{120-16\sqrt{58}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+16\sqrt{58}}{2*-16}=\frac{120+16\sqrt{58}}{-32}
$