C=(5a+7)(4a+1)

Solution for C=(5a+7)(4a+1) equation:

=(5C+7)(4C+1)

We move all terms to the left:

-((5C+7)(4C+1))=0

We multiply parentheses ..

-((+20C^2+5C+28C+7))=0


We calculate terms in parentheses: -((+20C^2+5C+28C+7)), so:

(+20C^2+5C+28C+7)

We get rid of parentheses

20C^2+5C+28C+7

We add all the numbers together, and all the variables

20C^2+33C+7

Back to the equation:

-(20C^2+33C+7)


We get rid of parentheses

-20C^2-33C-7=0

a = -20; b = -33; c = -7;
Δ = b2-4ac
Δ = -332-4·(-20)·(-7)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-23}{2*-20}=\frac{10}{-40}
=-1/4
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+23}{2*-20}=\frac{56}{-40}
=-1+2/5
$