-3/4k-1/2k=-20

Solution for -3/4k-1/2k=-20 equation:

-3/4k-1/2k=-20

We move all terms to the left:

-3/4k-1/2k-(-20)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We add all the numbers together, and all the variables

-3/4k-1/2k+20=0

We calculate fractions


(-6k)/8k^2+(-4k)/8k^2+20=0

We multiply all the terms by the denominator


(-6k)+(-4k)+20*8k^2=0

Wy multiply elements

160k^2+(-6k)+(-4k)=0

We get rid of parentheses

160k^2-6k-4k=0

We add all the numbers together, and all the variables

160k^2-10k=0

a = 160; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·160·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*160}=\frac{0}{320}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*160}=\frac{20}{320}
=1/16
$