Solve 30=45+27.4θ-600.7a^2

$$30 = 45 + 27.4 \theta - 600.7 a ^ { 2 }$$

Solve for θ

$$\theta =\frac{6007a^{2}}{274}-\frac{75}{137}$$

Steps for Solving Linear Equation

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

$$45+27.4\theta -600.7a^{2}=30$$

Subtract 45 from both sides.

$$27.4\theta -600.7a^{2}=30-45$$

Subtract 45 from 30 to get -15.

$$27.4\theta -600.7a^{2}=-15$$

Add 600.7a^{2} to both sides.

$$27.4\theta =-15+600.7a^{2}$$

The equation is in standard form.

$$27.4\theta =\frac{6007a^{2}}{10}-15$$

Divide both sides of the equation by 27.4, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{27.4\theta }{27.4}=\frac{\frac{6007a^{2}}{10}-15}{27.4}$$

Dividing by 27.4 undoes the multiplication by 27.4.

$$\theta =\frac{\frac{6007a^{2}}{10}-15}{27.4}$$

Divide -15+\frac{6007a^{2}}{10} by 27.4 by multiplying -15+\frac{6007a^{2}}{10} by the reciprocal of 27.4.

$$\theta =\frac{6007a^{2}}{274}-\frac{75}{137}$$

Solve for a (complex solution)

$$a=-\sqrt{\frac{274\theta +150}{6007}}$$

$$a=\sqrt{\frac{274\theta +150}{6007}}$$

Solve for a

$$a=\frac{\sqrt{\frac{1096\theta +600}{6007}}}{2}$$

$$a=-\frac{\sqrt{\frac{1096\theta +600}{6007}}}{2}\text{, }\theta \geq -\frac{75}{137}$$