-3/4k+5/2=3+4/9k

Solution for -3/4k+5/2=3+4/9k equation:

-3/4k+5/2=3+4/9k

We move all terms to the left:

-3/4k+5/2-(3+4/9k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 9k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-3/4k-(4/9k+3)+5/2=0

We get rid of parentheses

-3/4k-4/9k-3+5/2=0

We calculate fractions


1620k^2/144k^2+(-108k)/144k^2+(-64k)/144k^2-3=0

We multiply all the terms by the denominator


1620k^2+(-108k)+(-64k)-3*144k^2=0

Wy multiply elements

1620k^2-432k^2+(-108k)+(-64k)=0

We get rid of parentheses

1620k^2-432k^2-108k-64k=0

We add all the numbers together, and all the variables

1188k^2-172k=0

a = 1188; b = -172; c = 0;
Δ = b2-4ac
Δ = -1722-4·1188·0
Δ = 29584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29584}=172$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-172)-172}{2*1188}=\frac{0}{2376}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-172)+172}{2*1188}=\frac{344}{2376}
=43/297
$