Solve 0=a^2+4*1/2*a*b_{a}-10

$$0 = a ^ { 2 } + 4 \cdot \frac { 1 } { 2 } \cdot a \cdot b _ { a } - 10$$

Solve for b_a

$$b_{a}=-\frac{a}{2}+\frac{5}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply 4 and \frac{1}{2} to get 2.

$$0=a^{2}+2ab_{a}-10$$

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

$$a^{2}+2ab_{a}-10=0$$

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

$$2ab_{a}-10=-a^{2}$$

Add 10 to both sides.

$$2ab_{a}=-a^{2}+10$$

The equation is in standard form.

$$2ab_{a}=10-a^{2}$$

Divide both sides by 2a.

$$\frac{2ab_{a}}{2a}=\frac{10-a^{2}}{2a}$$

Dividing by 2a undoes the multiplication by 2a.

$$b_{a}=\frac{10-a^{2}}{2a}$$

Divide -a^{2}+10 by 2a.

$$b_{a}=-\frac{a}{2}+\frac{5}{a}$$

Solve for a

$$a=\sqrt{b_{a}^{2}+10}-b_{a}$$

$$a=-\sqrt{b_{a}^{2}+10}-b_{a}$$