5(x)=-0.2(x)^2+x+5.2

Solution for 5(x)=-0.2(x)^2+x+5.2 equation:

5(x)=-0.2(x)^2+x+5.2

We move all terms to the left:

5(x)-(-0.2(x)^2+x+5.2)=0

determiningTheFunctionDomain
-(-0.2x^2+x+5.2)+5x=0

We get rid of parentheses

0.2x^2-x+5x-5.2=0

We add all the numbers together, and all the variables

0.2x^2+4x-5.2=0

a = 0.2; b = 4; c = -5.2;
Δ = b2-4ac
Δ = 42-4·0.2·(-5.2)
Δ = 20.16
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{-(4)-\sqrt{20.16}}{2*0.2}=\frac{-4-\sqrt{20.16}}{0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+\sqrt{20.16}}{2*0.2}=\frac{-4+\sqrt{20.16}}{0.4}
$