0=w^2+1.5w-175

Solution for 0=w^2+1.5w-175 equation:

0=w^2+1.5w-175

We move all terms to the left:

0-(w^2+1.5w-175)=0

We add all the numbers together, and all the variables

-(w^2+1.5w-175)=0

We get rid of parentheses

-w^2-1.5w+175=0

We add all the numbers together, and all the variables

-1w^2-1.5w+175=0

a = -1; b = -1.5; c = +175;
Δ = b2-4ac
Δ = -1.52-4·(-1)·175
Δ = 702.25
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{702.25}}{2*-1}=\frac{1.5-\sqrt{702.25}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{702.25}}{2*-1}=\frac{1.5+\sqrt{702.25}}{-2}
$