x(x-29)+210=0

Solution for x(x-29)+210=0 equation:

x(x-29)+210=0

We multiply parentheses

x^2-29x+210=0

a = 1; b = -29; c = +210;
Δ = b2-4ac
Δ = -292-4·1·210
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-1}{2*1}=\frac{28}{2}
=14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+1}{2*1}=\frac{30}{2}
=15
$