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

Solution for 0=x^2+5x/2-9 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-x^2*2-5x+18=0

Wy multiply elements

-2x^2-5x+18=0

a = -2; b = -5; c = +18;
Δ = b2-4ac
Δ = -52-4·(-2)·18
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*-2}=\frac{18}{-4}
=-4+1/2
$