Solve alpha^2-0.8alpha+3.125beta=0

$$\alpha ^ { 2 } - 0.8 \alpha + 3.125 \beta = 0$$

Solve for β

$$\beta =-\frac{8\alpha \left(\alpha -0.8\right)}{25}$$

Steps for Solving Linear Equation

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

$$-0.8\alpha +3.125\beta =-\alpha ^{2}$$

Add 0.8\alpha to both sides.

$$3.125\beta =-\alpha ^{2}+0.8\alpha$$

The equation is in standard form.

$$3.125\beta =-\alpha ^{2}+\frac{4\alpha }{5}$$

Divide both sides of the equation by 3.125, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{3.125\beta }{3.125}=\frac{\alpha \left(0.8-\alpha \right)}{3.125}$$

Dividing by 3.125 undoes the multiplication by 3.125.

$$\beta =\frac{\alpha \left(0.8-\alpha \right)}{3.125}$$

Divide \alpha \left(0.8-\alpha \right) by 3.125 by multiplying \alpha \left(0.8-\alpha \right) by the reciprocal of 3.125.

$$\beta =\frac{8\alpha \left(0.8-\alpha \right)}{25}$$

Solve for α

$$\alpha =\frac{\sqrt{-\frac{25\beta }{2}+0.64}}{2}+0.4$$

$$\alpha =-\frac{\sqrt{-\frac{25\beta }{2}+0.64}}{2}+0.4\text{, }\beta \leq 0.0512$$