4n^2+9n=10

Solution for 4n^2+9n=10 equation:

4n^2+9n=10

We move all terms to the left:

4n^2+9n-(10)=0

a = 4; b = 9; c = -10;
Δ = b2-4ac
Δ = 92-4·4·(-10)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{241}}{2*4}=\frac{-9-\sqrt{241}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{241}}{2*4}=\frac{-9+\sqrt{241}}{8}
$