-3/2k+-9/8=3-7/8k

Solution for -3/2k+-9/8=3-7/8k equation:

-3/2k+-9/8=3-7/8k

We move all terms to the left:

-3/2k+-9/8-(3-7/8k)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 8k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-3/2k-(-7/8k+3)+-9/8=0

We add all the numbers together, and all the variables

-3/2k-(-7/8k+3)-9/8=0

We get rid of parentheses

-3/2k+7/8k-3-9/8=0

We calculate fractions


(-1536k)/1024k^2+14k/1024k^2+(-18k)/1024k^2-3=0

We multiply all the terms by the denominator


(-1536k)+14k+(-18k)-3*1024k^2=0

We add all the numbers together, and all the variables

14k+(-1536k)+(-18k)-3*1024k^2=0

Wy multiply elements

-3072k^2+14k+(-1536k)+(-18k)=0

We get rid of parentheses

-3072k^2+14k-1536k-18k=0

We add all the numbers together, and all the variables

-3072k^2-1540k=0

a = -3072; b = -1540; c = 0;
Δ = b2-4ac
Δ = -15402-4·(-3072)·0
Δ = 2371600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2371600}=1540$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1540)-1540}{2*-3072}=\frac{0}{-6144}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1540)+1540}{2*-3072}=\frac{3080}{-6144}
=-385/768
$