C(8)=2x(x+5)

Solution for C(8)=2x(x+5) equation:

(8)=2C(C+5)

We move all terms to the left:

(8)-(2C(C+5))=0


We calculate terms in parentheses: -(2C(C+5)), so:

2C(C+5)

We multiply parentheses

2C^2+10C

Back to the equation:

-(2C^2+10C)


We get rid of parentheses

-2C^2-10C+8=0

a = -2; b = -10; c = +8;
Δ = b2-4ac
Δ = -102-4·(-2)·8
Δ = 164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{41}}{2*-2}=\frac{10-2\sqrt{41}}{-4}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{41}}{2*-2}=\frac{10+2\sqrt{41}}{-4}
$