14x(30+x)=-196

Solution for 14x(30+x)=-196 equation:

14x(30+x)=-196

We move all terms to the left:

14x(30+x)-(-196)=0

We add all the numbers together, and all the variables

14x(x+30)-(-196)=0

We add all the numbers together, and all the variables

14x(x+30)+196=0

We multiply parentheses

14x^2+420x+196=0

a = 14; b = 420; c = +196;
Δ = b2-4ac
Δ = 4202-4·14·196
Δ = 165424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{165424}=\sqrt{784*211}=\sqrt{784}*\sqrt{211}=28\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-28\sqrt{211}}{2*14}=\frac{-420-28\sqrt{211}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+28\sqrt{211}}{2*14}=\frac{-420+28\sqrt{211}}{28}
$