4/5k-2(k+3)=-24

Solution for 4/5k-2(k+3)=-24 equation:

4/5k-2(k+3)=-24

We move all terms to the left:

4/5k-2(k+3)-(-24)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R


We add all the numbers together, and all the variables

4/5k-2(k+3)+24=0

We multiply parentheses

4/5k-2k-6+24=0

We multiply all the terms by the denominator


-2k*5k-6*5k+24*5k+4=0

Wy multiply elements

-10k^2-30k+120k+4=0

We add all the numbers together, and all the variables

-10k^2+90k+4=0

a = -10; b = 90; c = +4;
Δ = b2-4ac
Δ = 902-4·(-10)·4
Δ = 8260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8260}=\sqrt{4*2065}=\sqrt{4}*\sqrt{2065}=2\sqrt{2065}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2065}}{2*-10}=\frac{-90-2\sqrt{2065}}{-20}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2065}}{2*-10}=\frac{-90+2\sqrt{2065}}{-20}
$