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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+5x-2=0

a = 2; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·2·(-2)
Δ = 41
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{-(5)-\sqrt{41}}{2*2}=\frac{-5-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{41}}{2*2}=\frac{-5+\sqrt{41}}{4}
$