32(c2)=25(2c+3)

Solution for 32(c2)=25(2c+3) equation:

32(c2)=25(2c+3)

We move all terms to the left:

32(c2)-(25(2c+3))=0

We add all the numbers together, and all the variables

32c^2-(25(2c+3))=0


We calculate terms in parentheses: -(25(2c+3)), so:

25(2c+3)

We multiply parentheses

50c+75

Back to the equation:

-(50c+75)


We get rid of parentheses

32c^2-50c-75=0

a = 32; b = -50; c = -75;
Δ = b2-4ac
Δ = -502-4·32·(-75)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-110}{2*32}=\frac{-60}{64}
=-15/16
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+110}{2*32}=\frac{160}{64}
=2+1/2
$