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(3w-7)(5w-1)=0
We multiply parentheses ..
(+15w^2-3w-35w+7)=0
We get rid of parentheses
15w^2-3w-35w+7=0
We add all the numbers together, and all the variables
15w^2-38w+7=0
a = 15; b = -38; c = +7;
Δ = b2-4ac
Δ = -382-4·15·7
Δ = 1024
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1024}=32$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-32}{2*15}=\frac{6}{30} =1/5 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+32}{2*15}=\frac{70}{30} =2+1/3 $
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