0.55x+0.05x(6-x)=0.1(83)

Solution for 0.55x+0.05x(6-x)=0.1(83) equation:

0.55x+0.05x(6-x)=0.1(83)

We move all terms to the left:

0.55x+0.05x(6-x)-(0.1(83))=0

We add all the numbers together, and all the variables

0.55x+0.05x(-1x+6)-(0.183)=0

We add all the numbers together, and all the variables

0.55x+0.05x(-1x+6)-0.183=0

We multiply parentheses

0x^2+0.55x+0x-0.183=0

We add all the numbers together, and all the variables

x^2+1.55x-0.183=0

a = 1; b = 1.55; c = -0.183;
Δ = b2-4ac
Δ = 1.552-4·1·(-0.183)
Δ = 3.1345
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{-(1.55)-\sqrt{3.1345}}{2*1}=\frac{-1.55-\sqrt{3.1345}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.55)+\sqrt{3.1345}}{2*1}=\frac{-1.55+\sqrt{3.1345}}{2}
$