8x+3=15/8x

Solution for 8x+3=15/8x equation:

8x+3=15/8x

We move all terms to the left:

8x+3-(15/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+15/8x)+3=0

We get rid of parentheses

8x-15/8x+3=0

We multiply all the terms by the denominator


8x*8x+3*8x-15=0

Wy multiply elements

64x^2+24x-15=0

a = 64; b = 24; c = -15;
Δ = b2-4ac
Δ = 242-4·64·(-15)
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{69}}{2*64}=\frac{-24-8\sqrt{69}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{69}}{2*64}=\frac{-24+8\sqrt{69}}{128}
$