(3*x+7)(10*x-1)=0

Solution for (3*x+7)(10*x-1)=0 equation:

(3x+7)(10x-1)=0

We multiply parentheses ..

(+30x^2-3x+70x-7)=0

We get rid of parentheses

30x^2-3x+70x-7=0

We add all the numbers together, and all the variables

30x^2+67x-7=0

a = 30; b = 67; c = -7;
Δ = b2-4ac
Δ = 672-4·30·(-7)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-73}{2*30}=\frac{-140}{60}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+73}{2*30}=\frac{6}{60}
=1/10
$