3x+9=5x^2-1

Solution for 3x+9=5x^2-1 equation:

3x+9=5x^2-1

We move all terms to the left:

3x+9-(5x^2-1)=0

We get rid of parentheses

-5x^2+3x+1+9=0

We add all the numbers together, and all the variables

-5x^2+3x+10=0

a = -5; b = 3; c = +10;
Δ = b2-4ac
Δ = 32-4·(-5)·10
Δ = 209
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{-(3)-\sqrt{209}}{2*-5}=\frac{-3-\sqrt{209}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{209}}{2*-5}=\frac{-3+\sqrt{209}}{-10}
$