Solve -2x^2/9+k/2=(t+1)/4

$$- \frac { 2 x ^ { 2 } } { 9 } + \frac { k } { 2 } = \frac { ( t + 1 ) } { 4 }$$

Solve for k

$$k=\frac{4x^{2}}{9}+\frac{t}{2}+\frac{1}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 9,2,4.

$$-4\times 2x^{2}+18k=9\left(t+1\right)$$

Multiply -4 and 2 to get -8.

$$-8x^{2}+18k=9\left(t+1\right)$$

Use the distributive property to multiply 9 by t+1.

$$-8x^{2}+18k=9t+9$$

Add 8x^{2} to both sides.

$$18k=9t+9+8x^{2}$$

The equation is in standard form.

$$18k=8x^{2}+9t+9$$

Divide both sides by 18.

$$\frac{18k}{18}=\frac{8x^{2}+9t+9}{18}$$

Dividing by 18 undoes the multiplication by 18.

$$k=\frac{8x^{2}+9t+9}{18}$$

Divide 9t+9+8x^{2} by 18.

$$k=\frac{4x^{2}}{9}+\frac{t}{2}+\frac{1}{2}$$

Solve for t

$$t=-\frac{8x^{2}}{9}+2k-1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 9,2,4.

$$-4\times 2x^{2}+18k=9\left(t+1\right)$$

Multiply -4 and 2 to get -8.

$$-8x^{2}+18k=9\left(t+1\right)$$

Use the distributive property to multiply 9 by t+1.

$$-8x^{2}+18k=9t+9$$

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

$$9t+9=-8x^{2}+18k$$

Subtract 9 from both sides.

$$9t=-8x^{2}+18k-9$$

Divide both sides by 9.

$$\frac{9t}{9}=\frac{-8x^{2}+18k-9}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$t=\frac{-8x^{2}+18k-9}{9}$$

Divide -8x^{2}+18k-9 by 9.

$$t=-\frac{8x^{2}}{9}+2k-1$$