9x^2+5x=1

Solution for 9x^2+5x=1 equation:

9x^2+5x=1

We move all terms to the left:

9x^2+5x-(1)=0

a = 9; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·9·(-1)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{61}}{2*9}=\frac{-5-\sqrt{61}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{61}}{2*9}=\frac{-5+\sqrt{61}}{18}
$