(x+1.5)(x+1.5)=576

Solution for (x+1.5)(x+1.5)=576 equation:

(x+1.5)(x+1.5)=576

We move all terms to the left:

(x+1.5)(x+1.5)-(576)=0

We multiply parentheses ..

(+x^2+1.5x+1.5x+2.25)-576=0

We get rid of parentheses

x^2+1.5x+1.5x+2.25-576=0

We add all the numbers together, and all the variables

x^2+3x-573.75=0

a = 1; b = 3; c = -573.75;
Δ = b2-4ac
Δ = 32-4·1·(-573.75)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-48}{2*1}=\frac{-51}{2}
=-25+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+48}{2*1}=\frac{45}{2}
=22+1/2
$