(2x-5)(7x-1)=0

Solution for (2x-5)(7x-1)=0 equation:

(2x-5)(7x-1)=0

We multiply parentheses ..

(+14x^2-2x-35x+5)=0

We get rid of parentheses

14x^2-2x-35x+5=0

We add all the numbers together, and all the variables

14x^2-37x+5=0

a = 14; b = -37; c = +5;
Δ = b2-4ac
Δ = -372-4·14·5
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-33}{2*14}=\frac{4}{28}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+33}{2*14}=\frac{70}{28}
=2+1/2
$