-4x^2+1=5x+2

Solution for -4x^2+1=5x+2 equation:

-4x^2+1=5x+2

We move all terms to the left:

-4x^2+1-(5x+2)=0

We get rid of parentheses

-4x^2-5x-2+1=0

We add all the numbers together, and all the variables

-4x^2-5x-1=0

a = -4; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·(-4)·(-1)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*-4}=\frac{2}{-8}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*-4}=\frac{8}{-8}
=-1
$