5 k ^ { 2 } = 6 ( j - 20 k
Solve for j
j=\frac{5k\left(k+24\right)}{6}
Solve for k (complex solution)
k=\frac{\sqrt{30j+3600}}{5}-12
k=-\frac{\sqrt{30j+3600}}{5}-12
Solve for k
k=\frac{\sqrt{30j+3600}}{5}-12
k=-\frac{\sqrt{30j+3600}}{5}-12\text{, }j\geq -120
Share
Copied to clipboard
5k^{2}=6j-120k
Use the distributive property to multiply 6 by j-20k.
6j-120k=5k^{2}
Swap sides so that all variable terms are on the left hand side.
6j=5k^{2}+120k
Add 120k to both sides.
\frac{6j}{6}=\frac{5k\left(k+24\right)}{6}
Divide both sides by 6.
j=\frac{5k\left(k+24\right)}{6}
Dividing by 6 undoes the multiplication by 6.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}