3(5k+1)=(4k)2

Solution for 3(5k+1)=(4k)2 equation:

3(5k+1)=(4k)2

We move all terms to the left:

3(5k+1)-((4k)2)=0

determiningTheFunctionDomain
3(5k+1)-4k2=0

We add all the numbers together, and all the variables

-4k^2+3(5k+1)=0

We multiply parentheses

-4k^2+15k+3=0

a = -4; b = 15; c = +3;
Δ = b2-4ac
Δ = 152-4·(-4)·3
Δ = 273
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{-(15)-\sqrt{273}}{2*-4}=\frac{-15-\sqrt{273}}{-8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{273}}{2*-4}=\frac{-15+\sqrt{273}}{-8}
$