((66-x)x0.05)+0.06x=0.4

Solution for ((66-x)x0.05)+0.06x=0.4 equation:

((66-x)x0.05)+0.06x=0.4

We move all terms to the left:

((66-x)x0.05)+0.06x-(0.4)=0

We add all the numbers together, and all the variables

((-1x+66)x0.05)+0.06x-(0.4)=0

We add all the numbers together, and all the variables

0.06x+((-1x+66)x0.05)-0.4=0


We calculate terms in parentheses: +((-1x+66)x0.05), so:

(-1x+66)x0.05

We multiply parentheses

-1x^2+66x

Back to the equation:

+(-1x^2+66x)


We get rid of parentheses

-1x^2+66x+0.06x-0.4=0

We add all the numbers together, and all the variables

-1x^2+66.06x-0.4=0

a = -1; b = 66.06; c = -0.4;
Δ = b2-4ac
Δ = 66.062-4·(-1)·(-0.4)
Δ = 4362.3236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66.06)-\sqrt{4362.3236}}{2*-1}=\frac{-66.06-\sqrt{4362.3236}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66.06)+\sqrt{4362.3236}}{2*-1}=\frac{-66.06+\sqrt{4362.3236}}{-2}
$