2475=w(2w+10)

Solution for 2475=w(2w+10) equation:

2475=w(2w+10)

We move all terms to the left:

2475-(w(2w+10))=0


We calculate terms in parentheses: -(w(2w+10)), so:

w(2w+10)

We multiply parentheses

2w^2+10w

Back to the equation:

-(2w^2+10w)


We get rid of parentheses

-2w^2-10w+2475=0

a = -2; b = -10; c = +2475;
Δ = b2-4ac
Δ = -102-4·(-2)·2475
Δ = 19900
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:

$\sqrt{\Delta}=\sqrt{19900}=\sqrt{100*199}=\sqrt{100}*\sqrt{199}=10\sqrt{199}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{199}}{2*-2}=\frac{10-10\sqrt{199}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{199}}{2*-2}=\frac{10+10\sqrt{199}}{-4}
$