2x^2-5=-9/2

Solution for 2x^2-5=-9/2 equation:

2x^2-5=-9/2

We move all terms to the left:

2x^2-5-(-9/2)=0

We get rid of parentheses

2x^2-5+9/2=0

We multiply all the terms by the denominator


2x^2*2+9-5*2=0

We add all the numbers together, and all the variables

2x^2*2-1=0

Wy multiply elements

4x^2-1=0

a = 4; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·4·(-1)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*4}=\frac{4}{8}
=1/2
$