(35/100)*x=500

Solution for (35/100)*x=500 equation:

(35/100)*x=500

We move all terms to the left:

(35/100)*x-(500)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+35/100)*x-500=0

We multiply parentheses

35x^2-500=0

a = 35; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·35·(-500)
Δ = 70000
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:

$\sqrt{\Delta}=\sqrt{70000}=\sqrt{10000*7}=\sqrt{10000}*\sqrt{7}=100\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{7}}{2*35}=\frac{0-100\sqrt{7}}{70}
=-\frac{100\sqrt{7}}{70}
=-\frac{10\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{7}}{2*35}=\frac{0+100\sqrt{7}}{70}
=\frac{100\sqrt{7}}{70}
=\frac{10\sqrt{7}}{7}
$