14x^2=-1+9x

Solution for 14x^2=-1+9x equation:

14x^2=-1+9x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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