14x2+9x=-1

Solution for 14x2+9x=-1 equation:

14x^2+9x=-1

We move all terms to the left:

14x^2+9x-(-1)=0

We add all the numbers together, and all the variables

14x^2+9x+1=0

a = 14; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·14·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5}{2*14}=\frac{-14}{28}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5}{2*14}=\frac{-4}{28}
=-1/7
$