9x+1=10x^2

Solution for 9x+1=10x^2 equation:

9x+1=10x^2

We move all terms to the left:

9x+1-(10x^2)=0

determiningTheFunctionDomain
-10x^2+9x+1=0

a = -10; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·(-10)·1
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*-10}=\frac{-20}{-20}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*-10}=\frac{2}{-20}
=-1/10
$