2x^2-4=9x+1

Solution for 2x^2-4=9x+1 equation:

2x^2-4=9x+1

We move all terms to the left:

2x^2-4-(9x+1)=0

We get rid of parentheses

2x^2-9x-1-4=0

We add all the numbers together, and all the variables

2x^2-9x-5=0

a = 2; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·2·(-5)
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*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*2}=\frac{20}{4}
=5
$