7x2+1=9x

Solution for 7x2+1=9x equation:

7x^2+1=9x

We move all terms to the left:

7x^2+1-(9x)=0

a = 7; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·7·1
Δ = 53
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{-(-9)-\sqrt{53}}{2*7}=\frac{9-\sqrt{53}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{53}}{2*7}=\frac{9+\sqrt{53}}{14}
$