1.48E^-6=(2x)^2/1.8-x

Solution for 1.48E^-6=(2x)^2/1.8-x equation:

1.48^-6=(2E)^2/1.8-E

We move all terms to the left:

1.48^-6-((2E)^2/1.8-E)=0


Domain of the equation: 1.8-E)!=0

We move all terms containing E to the left, all other terms to the right

-E)!=-1.8

E!=-1.8/1

E!=-1.8

E∈R


We add all the numbers together, and all the variables

-(2E^2/1.8-E)=0

We get rid of parentheses

-2E^2/1.8+E=0

We multiply all the terms by the denominator


-2E^2+E*1.8=0

Wy multiply elements

-2E^2+1.8E=0

a = -2; b = 1.8; c = 0;
Δ = b2-4ac
Δ = 1.82-4·(-2)·0
Δ = 3.24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.8)-\sqrt{3.24}}{2*-2}=\frac{-1.8-\sqrt{3.24}}{-4}
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.8)+\sqrt{3.24}}{2*-2}=\frac{-1.8+\sqrt{3.24}}{-4}
$