Solve 2z^2+z-10s=0

$$2 z ^ { 2 } + z - 10 s = 0$$

Solve for s

$$s=\frac{z\left(2z+1\right)}{10}$$

Steps for Solving Linear Equation

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

$$z-10s=-2z^{2}$$

Subtract z from both sides.

$$-10s=-2z^{2}-z$$

Divide both sides by -10.

$$\frac{-10s}{-10}=-\frac{z\left(2z+1\right)}{-10}$$

Dividing by -10 undoes the multiplication by -10.

$$s=-\frac{z\left(2z+1\right)}{-10}$$

Divide -z\left(1+2z\right) by -10.

$$s=\frac{z\left(2z+1\right)}{10}$$

Solve for z

$$z=\frac{\sqrt{80s+1}-1}{4}$$

$$z=\frac{-\sqrt{80s+1}-1}{4}\text{, }s\geq -\frac{1}{80}$$