16/25x+18=x

Solution for 16/25x+18=x equation:

16/25x+18=x

We move all terms to the left:

16/25x+18-(x)=0


Domain of the equation: 25x!=0

x!=0/25

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+16/25x+18=0

We multiply all the terms by the denominator


-1x*25x+18*25x+16=0

Wy multiply elements

-25x^2+450x+16=0

a = -25; b = 450; c = +16;
Δ = b2-4ac
Δ = 4502-4·(-25)·16
Δ = 204100
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:

$\sqrt{\Delta}=\sqrt{204100}=\sqrt{100*2041}=\sqrt{100}*\sqrt{2041}=10\sqrt{2041}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-10\sqrt{2041}}{2*-25}=\frac{-450-10\sqrt{2041}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+10\sqrt{2041}}{2*-25}=\frac{-450+10\sqrt{2041}}{-50}
$