45+3/8x=x

Solution for 45+3/8x=x equation:

45+3/8x=x

We move all terms to the left:

45+3/8x-(x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/8x+45=0

We multiply all the terms by the denominator


-1x*8x+45*8x+3=0

Wy multiply elements

-8x^2+360x+3=0

a = -8; b = 360; c = +3;
Δ = b2-4ac
Δ = 3602-4·(-8)·3
Δ = 129696
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:

$\sqrt{\Delta}=\sqrt{129696}=\sqrt{16*8106}=\sqrt{16}*\sqrt{8106}=4\sqrt{8106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-4\sqrt{8106}}{2*-8}=\frac{-360-4\sqrt{8106}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+4\sqrt{8106}}{2*-8}=\frac{-360+4\sqrt{8106}}{-16}
$