Solve 11/2(28)=2/5t^2+1/3(-36)

$$1 \frac { 1 } { 2 } ( 28 ) = \frac { 2 } { 5 } t ^ { 2 } + \frac { 1 } { 3 } ( - 36 )$$

Solve for t

$$t=3\sqrt{15}\approx 11.618950039$$

$$t=-3\sqrt{15}\approx -11.618950039$$

Steps by Finding Square Root

Multiply both sides of the equation by 30, the least common multiple of 2,5,3.

$$15\left(1\times 2+1\right)\times 28=12t^{2}+10\left(-36\right)$$

Multiply 1 and 2 to get 2.

$$15\left(2+1\right)\times 28=12t^{2}+10\left(-36\right)$$

Add 2 and 1 to get 3.

$$15\times 3\times 28=12t^{2}+10\left(-36\right)$$

Multiply 15 and 3 to get 45.

$$45\times 28=12t^{2}+10\left(-36\right)$$

Multiply 45 and 28 to get 1260.

$$1260=12t^{2}+10\left(-36\right)$$

Multiply 10 and -36 to get -360.

$$1260=12t^{2}-360$$

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

$$12t^{2}-360=1260$$

Add 360 to both sides.

$$12t^{2}=1260+360$$

Add 1260 and 360 to get 1620.

$$12t^{2}=1620$$

Divide both sides by 12.

$$t^{2}=\frac{1620}{12}$$

Divide 1620 by 12 to get 135.

$$t^{2}=135$$

Take the square root of both sides of the equation.

$$t=3\sqrt{15} t=-3\sqrt{15}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 30, the least common multiple of 2,5,3.

$$15\left(1\times 2+1\right)\times 28=12t^{2}+10\left(-36\right)$$

Multiply 1 and 2 to get 2.

$$15\left(2+1\right)\times 28=12t^{2}+10\left(-36\right)$$

Add 2 and 1 to get 3.

$$15\times 3\times 28=12t^{2}+10\left(-36\right)$$

Multiply 15 and 3 to get 45.

$$45\times 28=12t^{2}+10\left(-36\right)$$

Multiply 45 and 28 to get 1260.

$$1260=12t^{2}+10\left(-36\right)$$

Multiply 10 and -36 to get -360.

$$1260=12t^{2}-360$$

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

$$12t^{2}-360=1260$$

Subtract 1260 from both sides.

$$12t^{2}-360-1260=0$$

Subtract 1260 from -360 to get -1620.

$$12t^{2}-1620=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -1620 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 12\left(-1620\right)}}{2\times 12}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 12\left(-1620\right)}}{2\times 12}$$

Multiply -4 times 12.

$$t=\frac{0±\sqrt{-48\left(-1620\right)}}{2\times 12}$$

Multiply -48 times -1620.

$$t=\frac{0±\sqrt{77760}}{2\times 12}$$

Take the square root of 77760.

$$t=\frac{0±72\sqrt{15}}{2\times 12}$$

Multiply 2 times 12.

$$t=\frac{0±72\sqrt{15}}{24}$$

Now solve the equation t=\frac{0±72\sqrt{15}}{24} when ± is plus.

$$t=3\sqrt{15}$$

Now solve the equation t=\frac{0±72\sqrt{15}}{24} when ± is minus.

$$t=-3\sqrt{15}$$

The equation is now solved.

$$t=3\sqrt{15} t=-3\sqrt{15}$$