(X+2.5)(x+2.5)=8.25

Solution for (X+2.5)(x+2.5)=8.25 equation:

(X+2.5)(X+2.5)=8.25

We move all terms to the left:

(X+2.5)(X+2.5)-(8.25)=0

We add all the numbers together, and all the variables

(X+2.5)(X+2.5)-8.25=0

We multiply parentheses ..

(+X^2+2.5X+2.5X+6.25)-8.25=0

We get rid of parentheses

X^2+2.5X+2.5X+6.25-8.25=0

We add all the numbers together, and all the variables

X^2+5X-2=0

a = 1; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·1·(-2)
Δ = 33
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{33}}{2*1}=\frac{-5-\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*1}=\frac{-5+\sqrt{33}}{2}
$