0=w*w+1.5w-13.5

Solution for 0=w*w+1.5w-13.5 equation:

0=w*w+1.5w-13.5

We move all terms to the left:

0-(w*w+1.5w-13.5)=0

We add all the numbers together, and all the variables

-(1.5w+w*w-13.5)+0=0

We add all the numbers together, and all the variables

-(1.5w+w*w-13.5)=0

We get rid of parentheses

-1.5w-w*w+13.5=0

Wy multiply elements

-1w^2-1.5w+13.5=0

a = -1; b = -1.5; c = +13.5;
Δ = b2-4ac
Δ = -1.52-4·(-1)·13.5
Δ = 56.25
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{-(-1.5)-\sqrt{56.25}}{2*-1}=\frac{1.5-\sqrt{56.25}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{56.25}}{2*-1}=\frac{1.5+\sqrt{56.25}}{-2}
$