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(5x-3)(7x-1)=0
We multiply parentheses ..
(+35x^2-5x-21x+3)=0
We get rid of parentheses
35x^2-5x-21x+3=0
We add all the numbers together, and all the variables
35x^2-26x+3=0
a = 35; b = -26; c = +3;
Δ = b2-4ac
Δ = -262-4·35·3
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{256}=16$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-16}{2*35}=\frac{10}{70} =1/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+16}{2*35}=\frac{42}{70} =3/5 $
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