Solve 1500/a+1200a/8a+240=150

$$\frac { 1500 } { a } + \frac { 1200 a } { 8 a + 240 } = 150$$

Solve for a

$$a=15$$

Steps for Solving Linear Equation

Variable a cannot be equal to any of the values -30,0 since division by zero is not defined. Multiply both sides of the equation by 8a\left(a+30\right), the least common multiple of a,8a+240.

$$\left(8a+240\right)\times 1500+a\times 1200a=1200a\left(a+30\right)$$

Use the distributive property to multiply 8a+240 by 1500.

$$12000a+360000+a\times 1200a=1200a\left(a+30\right)$$

Multiply a and a to get a^{2}.

$$12000a+360000+a^{2}\times 1200=1200a\left(a+30\right)$$

Use the distributive property to multiply 1200a by a+30.

$$12000a+360000+a^{2}\times 1200=1200a^{2}+36000a$$

Subtract 1200a^{2} from both sides.

$$12000a+360000+a^{2}\times 1200-1200a^{2}=36000a$$

Combine a^{2}\times 1200 and -1200a^{2} to get 0.

$$12000a+360000=36000a$$

Subtract 36000a from both sides.

$$12000a+360000-36000a=0$$

Combine 12000a and -36000a to get -24000a.

$$-24000a+360000=0$$

Subtract 360000 from both sides. Anything subtracted from zero gives its negation.

$$-24000a=-360000$$

Divide both sides by -24000.

$$a=\frac{-360000}{-24000}$$

Divide -360000 by -24000 to get 15.

$$a=15$$