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(7w-7)(3w+7)=180
We move all terms to the left:
(7w-7)(3w+7)-(180)=0
We multiply parentheses ..
(+21w^2+49w-21w-49)-180=0
We get rid of parentheses
21w^2+49w-21w-49-180=0
We add all the numbers together, and all the variables
21w^2+28w-229=0
a = 21; b = 28; c = -229;
Δ = b2-4ac
Δ = 282-4·21·(-229)
Δ = 20020
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20020}=\sqrt{4*5005}=\sqrt{4}*\sqrt{5005}=2\sqrt{5005}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{5005}}{2*21}=\frac{-28-2\sqrt{5005}}{42} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{5005}}{2*21}=\frac{-28+2\sqrt{5005}}{42} $
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