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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

16x^2-7=0

a = 16; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·16·(-7)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*16}=\frac{0-8\sqrt{7}}{32}
=-\frac{8\sqrt{7}}{32}
=-\frac{\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*16}=\frac{0+8\sqrt{7}}{32}
=\frac{8\sqrt{7}}{32}
=\frac{\sqrt{7}}{4}
$