(2.5x+1)(2.5x+1)=9

Solution for (2.5x+1)(2.5x+1)=9 equation:

(2.5x+1)(2.5x+1)=9

We move all terms to the left:

(2.5x+1)(2.5x+1)-(9)=0

We multiply parentheses ..

(+4x^2+2x+2x+1)-9=0

We get rid of parentheses

4x^2+2x+2x+1-9=0

We add all the numbers together, and all the variables

4x^2+4x-8=0

a = 4; b = 4; c = -8;
Δ = b2-4ac
Δ = 42-4·4·(-8)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*4}=\frac{8}{8}
=1
$