3/4k+7/10=11/15k-2

Solution for 3/4k+7/10=11/15k-2 equation:

3/4k+7/10=11/15k-2

We move all terms to the left:

3/4k+7/10-(11/15k-2)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 15k-2)!=0

k∈R


We get rid of parentheses

3/4k-11/15k+2+7/10=0

We calculate fractions


420k^2/600k^2+450k/600k^2+(-440k)/600k^2+2=0

We multiply all the terms by the denominator


420k^2+450k+(-440k)+2*600k^2=0

Wy multiply elements

420k^2+1200k^2+450k+(-440k)=0

We get rid of parentheses

420k^2+1200k^2+450k-440k=0

We add all the numbers together, and all the variables

1620k^2+10k=0

a = 1620; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·1620·0
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*1620}=\frac{-20}{3240}
=-1/162
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*1620}=\frac{0}{3240}
=0
$