25c(0.5c)=86.3(40-c)

Solution for 25c(0.5c)=86.3(40-c) equation:

25c(0.5c)=86.3(40-c)

We move all terms to the left:

25c(0.5c)-(86.3(40-c))=0

We add all the numbers together, and all the variables

25c(+0.5c)-(86.3(-1c+40))=0

We multiply parentheses

0c^2-(86.3(-1c+40))=0


We calculate terms in parentheses: -(86.3(-1c+40)), so:

86.3(-1c+40)

We multiply parentheses

-86.3c+3452

Back to the equation:

-(-86.3c+3452)


We add all the numbers together, and all the variables

c^2-(-86.3c+3452)=0

We get rid of parentheses

c^2+86.3c-3452=0

a = 1; b = 86.3; c = -3452;
Δ = b2-4ac
Δ = 86.32-4·1·(-3452)
Δ = 21255.69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86.3)-\sqrt{21255.69}}{2*1}=\frac{-86.3-\sqrt{21255.69}}{2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86.3)+\sqrt{21255.69}}{2*1}=\frac{-86.3+\sqrt{21255.69}}{2}
$