16/100*x-x=426

Solution for 16/100*x-x=426 equation:

16/100x-x=426

We move all terms to the left:

16/100x-x-(426)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+16/100x-426=0

We multiply all the terms by the denominator


-1x*100x-426*100x+16=0

Wy multiply elements

-100x^2-42600x+16=0

a = -100; b = -42600; c = +16;
Δ = b2-4ac
Δ = -426002-4·(-100)·16
Δ = 1814766400
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:

$\sqrt{\Delta}=\sqrt{1814766400}=\sqrt{1600*1134229}=\sqrt{1600}*\sqrt{1134229}=40\sqrt{1134229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42600)-40\sqrt{1134229}}{2*-100}=\frac{42600-40\sqrt{1134229}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42600)+40\sqrt{1134229}}{2*-100}=\frac{42600+40\sqrt{1134229}}{-200}
$