(5x+1)(14x+7)=0

Solution for (5x+1)(14x+7)=0 equation:

(5x+1)(14x+7)=0

We multiply parentheses ..

(+70x^2+35x+14x+7)=0

We get rid of parentheses

70x^2+35x+14x+7=0

We add all the numbers together, and all the variables

70x^2+49x+7=0

a = 70; b = 49; c = +7;
Δ = b2-4ac
Δ = 492-4·70·7
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-21}{2*70}=\frac{-70}{140}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+21}{2*70}=\frac{-28}{140}
=-1/5
$