9,600=60/100x+x

Solution for 9,600=60/100x+x equation:

9.600=60/100x+x

We move all terms to the left:

9.600-(60/100x+x)=0


Domain of the equation: 100x+x)!=0

x∈R


We add all the numbers together, and all the variables

-(+x+60/100x)+9.600=0

We add all the numbers together, and all the variables

-(+x+60/100x)+9.6=0

We get rid of parentheses

-x-60/100x+9.6=0

We multiply all the terms by the denominator


-x*100x+(9.6)*100x-60=0

We multiply parentheses

-x*100x+960x-60=0

Wy multiply elements

-100x^2+960x-60=0

a = -100; b = 960; c = -60;
Δ = b2-4ac
Δ = 9602-4·(-100)·(-60)
Δ = 897600
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:

$\sqrt{\Delta}=\sqrt{897600}=\sqrt{1600*561}=\sqrt{1600}*\sqrt{561}=40\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(960)-40\sqrt{561}}{2*-100}=\frac{-960-40\sqrt{561}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(960)+40\sqrt{561}}{2*-100}=\frac{-960+40\sqrt{561}}{-200}
$