3z(z-10)+(z+10)=0

Solution for 3z(z-10)+(z+10)=0 equation:

3z(z-10)+(z+10)=0

We multiply parentheses

3z^2-30z+(z+10)=0

We get rid of parentheses

3z^2-30z+z+10=0

We add all the numbers together, and all the variables

3z^2-29z+10=0

a = 3; b = -29; c = +10;
Δ = b2-4ac
Δ = -292-4·3·10
Δ = 721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{721}}{2*3}=\frac{29-\sqrt{721}}{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{721}}{2*3}=\frac{29+\sqrt{721}}{6}
$