12500=(3w-30)(w-30)15

Solution for 12500=(3w-30)(w-30)15 equation:

12500=(3w-30)(w-30)15

We move all terms to the left:

12500-((3w-30)(w-30)15)=0

We multiply parentheses ..

-((+3w^2-90w-30w+900)15)+12500=0


We calculate terms in parentheses: -((+3w^2-90w-30w+900)15), so:

(+3w^2-90w-30w+900)15

We multiply parentheses

45w^2-1350w-450w+13500

We add all the numbers together, and all the variables

45w^2-1800w+13500

Back to the equation:

-(45w^2-1800w+13500)


We get rid of parentheses

-45w^2+1800w-13500+12500=0

We add all the numbers together, and all the variables

-45w^2+1800w-1000=0

a = -45; b = 1800; c = -1000;
Δ = b2-4ac
Δ = 18002-4·(-45)·(-1000)
Δ = 3060000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3060000}=\sqrt{90000*34}=\sqrt{90000}*\sqrt{34}=300\sqrt{34}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1800)-300\sqrt{34}}{2*-45}=\frac{-1800-300\sqrt{34}}{-90}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1800)+300\sqrt{34}}{2*-45}=\frac{-1800+300\sqrt{34}}{-90}
$