a^2/0.2-a=0.00001.8

Solution for a^2/0.2-a=0.00001.8 equation:

a^2/0.2-a=0.00001.8

We move all terms to the left:

a^2/0.2-a-(0.00001.8)=0

We add all the numbers together, and all the variables

a^2/0.2-a-(8.0E-6)=0

We add all the numbers together, and all the variables

a^2/0.2-1a-15.746254627672=0

We multiply all the terms by the denominator


a^2-1a*0.2-(15.746254627672)*0.2=0

We add all the numbers together, and all the variables

a^2-1a*0.2-3.1492509255344=0

Wy multiply elements

a^2-0.2a-3.1492509255344=0

a = 1; b = -0.2; c = -3.1492509255344;
Δ = b2-4ac
Δ = -0.22-4·1·(-3.1492509255344)
Δ = 12.637003702138
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.2)-\sqrt{12.637003702138}}{2*1}=\frac{0.2-\sqrt{12.637003702138}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{12.637003702138}}{2*1}=\frac{0.2+\sqrt{12.637003702138}}{2}
$