2*x=7/8x-15

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

2x=7/8x-15

We move all terms to the left:

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


Domain of the equation: 8x-15)!=0

x∈R


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 = 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}
$