(3x+5)(7x+1)=0

Solution for (3x+5)(7x+1)=0 equation:

(3x+5)(7x+1)=0

We multiply parentheses ..

(+21x^2+3x+35x+5)=0

We get rid of parentheses

21x^2+3x+35x+5=0

We add all the numbers together, and all the variables

21x^2+38x+5=0

a = 21; b = 38; c = +5;
Δ = b2-4ac
Δ = 382-4·21·5
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-32}{2*21}=\frac{-70}{42}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+32}{2*21}=\frac{-6}{42}
=-1/7
$