(1000+5x)x/100=91.80

Solution for (1000+5x)x/100=91.80 equation:

(1000+5x)x/100=91.80

We move all terms to the left:

(1000+5x)x/100-(91.80)=0

We add all the numbers together, and all the variables

(5x+1000)x/100-(91.8)=0

We add all the numbers together, and all the variables

(5x+1000)x/100-91.8=0

We multiply all the terms by the denominator


(5x+1000)x-(91.8)*100=0

We add all the numbers together, and all the variables

(5x+1000)x-9180=0

We multiply parentheses

5x^2+1000x-9180=0

a = 5; b = 1000; c = -9180;
Δ = b2-4ac
Δ = 10002-4·5·(-9180)
Δ = 1183600
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:

$\sqrt{\Delta}=\sqrt{1183600}=\sqrt{400*2959}=\sqrt{400}*\sqrt{2959}=20\sqrt{2959}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-20\sqrt{2959}}{2*5}=\frac{-1000-20\sqrt{2959}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+20\sqrt{2959}}{2*5}=\frac{-1000+20\sqrt{2959}}{10}
$