41=0.05(x^2-41x)

Solution for 41=0.05(x^2-41x) equation:

41=0.05(x^2-41x)

We move all terms to the left:

41-(0.05(x^2-41x))=0


We calculate terms in parentheses: -(0.05(x^2-41x)), so:

0.05(x^2-41x)

We multiply parentheses

0.05x^2-2.05x

Back to the equation:

-(0.05x^2-2.05x)


We get rid of parentheses

-0.05x^2+2.05x+41=0

a = -0.05; b = 2.05; c = +41;
Δ = b2-4ac
Δ = 2.052-4·(-0.05)·41
Δ = 12.4025
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{-(2.05)-\sqrt{12.4025}}{2*-0.05}=\frac{-2.05-\sqrt{12.4025}}{-0.1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.05)+\sqrt{12.4025}}{2*-0.05}=\frac{-2.05+\sqrt{12.4025}}{-0.1}
$