(10x-3)(5x+1)=0

Solution for (10x-3)(5x+1)=0 equation:

(10x-3)(5x+1)=0

We multiply parentheses ..

(+50x^2+10x-15x-3)=0

We get rid of parentheses

50x^2+10x-15x-3=0

We add all the numbers together, and all the variables

50x^2-5x-3=0

a = 50; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·50·(-3)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-25}{2*50}=\frac{-20}{100}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+25}{2*50}=\frac{30}{100}
=3/10
$