k-8.3+2.4k=-3/4k

Solution for k-8.3+2.4k=-3/4k equation:

k-8.3+2.4k=-3/4k

We move all terms to the left:

k-8.3+2.4k-(-3/4k)=0


Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3.4k-(-3/4k)-8.3=0

We get rid of parentheses

3.4k+3/4k-8.3=0

We multiply all the terms by the denominator


(3.4k)*4k-(8.3)*4k+3=0

We add all the numbers together, and all the variables

(+3.4k)*4k-(8.3)*4k+3=0

We multiply parentheses

12k^2-33.2k+3=0

a = 12; b = -33.2; c = +3;
Δ = b2-4ac
Δ = -33.22-4·12·3
Δ = 958.24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33.2)-\sqrt{958.24}}{2*12}=\frac{33.2-\sqrt{958.24}}{24}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33.2)+\sqrt{958.24}}{2*12}=\frac{33.2+\sqrt{958.24}}{24}
$