(w-1.5)(w-1.5)=352.25

Solution for (w-1.5)(w-1.5)=352.25 equation:

(w-1.5)(w-1.5)=352.25

We move all terms to the left:

(w-1.5)(w-1.5)-(352.25)=0

We add all the numbers together, and all the variables

(w-1.5)(w-1.5)-352.25=0

We multiply parentheses ..

(+w^2-1.5w-1.5w+2.25)-352.25=0

We get rid of parentheses

w^2-1.5w-1.5w+2.25-352.25=0

We add all the numbers together, and all the variables

w^2-3w-350=0

a = 1; b = -3; c = -350;
Δ = b2-4ac
Δ = -32-4·1·(-350)
Δ = 1409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{1409}}{2*1}=\frac{3-\sqrt{1409}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1409}}{2*1}=\frac{3+\sqrt{1409}}{2}
$