4500/e=30e=

Solution for 4500/e=30e= equation:

4500/e=30e=

We move all terms to the left:

4500/e-(30e)=0


Domain of the equation: e!=0

e∈R


We add all the numbers together, and all the variables

-30e+4500/e=0

We multiply all the terms by the denominator


-30e*e+4500=0

Wy multiply elements

-30e^2+4500=0

a = -30; b = 0; c = +4500;
Δ = b2-4ac
Δ = 02-4·(-30)·4500
Δ = 540000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{540000}=\sqrt{90000*6}=\sqrt{90000}*\sqrt{6}=300\sqrt{6}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{6}}{2*-30}=\frac{0-300\sqrt{6}}{-60}
=-\frac{300\sqrt{6}}{-60}
=-\frac{5\sqrt{6}}{-1}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{6}}{2*-30}=\frac{0+300\sqrt{6}}{-60}
=\frac{300\sqrt{6}}{-60}
=\frac{5\sqrt{6}}{-1}
$