x=15/32x*2

Solution for x=15/32x*2 equation:

x=15/32x*2

We move all terms to the left:

x-(15/32x*2)=0


Domain of the equation: 32x*2)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+15/32x*2)=0

We get rid of parentheses

x-15/32x*2=0

We multiply all the terms by the denominator


x*32x*2-15=0

Wy multiply elements

64x^2*2-15=0

Wy multiply elements

128x^2-15=0

a = 128; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·128·(-15)
Δ = 7680
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:

$\sqrt{\Delta}=\sqrt{7680}=\sqrt{256*30}=\sqrt{256}*\sqrt{30}=16\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{30}}{2*128}=\frac{0-16\sqrt{30}}{256}
=-\frac{16\sqrt{30}}{256}
=-\frac{\sqrt{30}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{30}}{2*128}=\frac{0+16\sqrt{30}}{256}
=\frac{16\sqrt{30}}{256}
=\frac{\sqrt{30}}{16}
$