3/4c+1/2c=8/9

Solution for 3/4c+1/2c=8/9 equation:

3/4c+1/2c=8/9

We move all terms to the left:

3/4c+1/2c-(8/9)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R



Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

3/4c+1/2c-(+8/9)=0

We get rid of parentheses

3/4c+1/2c-8/9=0

We calculate fractions


(-128c^2)/648c^2+486c/648c^2+324c/648c^2=0

We multiply all the terms by the denominator


(-128c^2)+486c+324c=0

We add all the numbers together, and all the variables

(-128c^2)+810c=0

We get rid of parentheses

-128c^2+810c=0

a = -128; b = 810; c = 0;
Δ = b2-4ac
Δ = 8102-4·(-128)·0
Δ = 656100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{656100}=810$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(810)-810}{2*-128}=\frac{-1620}{-256}
=6+21/64
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(810)+810}{2*-128}=\frac{0}{-256}
=0
$