Solve 3x^2+b/2-5=0

$$3 x ^ { 2 } + \frac { b } { 2 } - 5 = 0$$

Solve for b

$$b=10-6x^{2}$$

Solution Steps

Multiply both sides of the equation by 2.

$$6x^{2}+b-10=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$b-10=-6x^{2}$$

Add 10 to both sides.

$$b=-6x^{2}+10$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{60-6b}}{6}$$

$$x=\frac{\sqrt{60-6b}}{6}$$

Solve for x

$$x=\frac{\sqrt{60-6b}}{6}$$

$$x=-\frac{\sqrt{60-6b}}{6}\text{, }b\leq 10$$