2w2-7w-3=(w-3)2

Solution for 2w2-7w-3=(w-3)2 equation:

2w^2-7w-3=(w-3)2

We move all terms to the left:

2w^2-7w-3-((w-3)2)=0


We calculate terms in parentheses: -((w-3)2), so:

(w-3)2

We multiply parentheses

2w-6

Back to the equation:

-(2w-6)


We get rid of parentheses

2w^2-7w-2w+6-3=0

We add all the numbers together, and all the variables

2w^2-9w+3=0

a = 2; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·2·3
Δ = 57
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{-(-9)-\sqrt{57}}{2*2}=\frac{9-\sqrt{57}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*2}=\frac{9+\sqrt{57}}{4}
$