14x^2=-27x

Solution for 14x^2=-27x equation:

14x^2=-27x

We move all terms to the left:

14x^2-(-27x)=0

We get rid of parentheses

14x^2+27x=0

a = 14; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·14·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*14}=\frac{-54}{28}
=-1+13/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*14}=\frac{0}{28}
=0
$