Solve 4s^2(-5u)=(3t-4(3)/5)

$$4 s ^ { 2 } ( - 5 u ) = ( \frac { 3 t - 4 ( 3 ) } { 5 } )$$

Solve for t

$$t=-\frac{100us^{2}}{3}+4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$20s^{2}\left(-5\right)u=3t-4\times 3$$

Multiply 20 and -5 to get -100.

$$-100s^{2}u=3t-4\times 3$$

Multiply 4 and 3 to get 12.

$$-100s^{2}u=3t-12$$

Swap sides so that all variable terms are on the left hand side.

$$3t-12=-100s^{2}u$$

Add 12 to both sides.

$$3t=-100s^{2}u+12$$

The equation is in standard form.

$$3t=12-100us^{2}$$

Divide both sides by 3.

$$\frac{3t}{3}=\frac{12-100us^{2}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$t=\frac{12-100us^{2}}{3}$$

Divide -100s^{2}u+12 by 3.

$$t=-\frac{100us^{2}}{3}+4$$

Solve for s (complex solution)

$$\left\{\begin{matrix}s=-\frac{iu^{-\frac{1}{2}}\sqrt{3\left(t-4\right)}}{10}\text{; }s=\frac{iu^{-\frac{1}{2}}\sqrt{3\left(t-4\right)}}{10}\text{, }&u\neq 0\\s\in \mathrm{C}\text{, }&t=4\text{ and }u=0\end{matrix}\right.$$

Solve for s

$$\left\{\begin{matrix}s=\frac{\sqrt{-\frac{3\left(t-4\right)}{u}}}{10}\text{; }s=-\frac{\sqrt{-\frac{3\left(t-4\right)}{u}}}{10}\text{, }&\left(u>0\text{ and }t\leq 4\right)\text{ or }\left(t\geq 4\text{ and }u<0\right)\\s\in \mathrm{R}\text{, }&t=4\text{ and }u=0\end{matrix}\right.$$