x+5/100*x=300

Solution for x+5/100*x=300 equation:

x+5/100x=300

We move all terms to the left:

x+5/100x-(300)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-300*100x+5=0

Wy multiply elements

100x^2-30000x+5=0

a = 100; b = -30000; c = +5;
Δ = b2-4ac
Δ = -300002-4·100·5
Δ = 899998000
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:

$\sqrt{\Delta}=\sqrt{899998000}=\sqrt{48400*18595}=\sqrt{48400}*\sqrt{18595}=220\sqrt{18595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30000)-220\sqrt{18595}}{2*100}=\frac{30000-220\sqrt{18595}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30000)+220\sqrt{18595}}{2*100}=\frac{30000+220\sqrt{18595}}{200}
$