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(7x+1)(5x+1)=0
We multiply parentheses ..
(+35x^2+7x+5x+1)=0
We get rid of parentheses
35x^2+7x+5x+1=0
We add all the numbers together, and all the variables
35x^2+12x+1=0
a = 35; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·35·1
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2}{2*35}=\frac{-14}{70} =-1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2}{2*35}=\frac{-10}{70} =-1/7 $
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