(2x-3)(x+2)=22.5

Solution for (2x-3)(x+2)=22.5 equation:

(2x-3)(x+2)=22.5

We move all terms to the left:

(2x-3)(x+2)-(22.5)=0

We add all the numbers together, and all the variables

(2x-3)(x+2)-22.5=0

We multiply parentheses ..

(+2x^2+4x-3x-6)-22.5=0

We get rid of parentheses

2x^2+4x-3x-6-22.5=0

We add all the numbers together, and all the variables

2x^2+x-28.5=0

a = 2; b = 1; c = -28.5;
Δ = b2-4ac
Δ = 12-4·2·(-28.5)
Δ = 229
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{-(1)-\sqrt{229}}{2*2}=\frac{-1-\sqrt{229}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{229}}{2*2}=\frac{-1+\sqrt{229}}{4}
$