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

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

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

We multiply parentheses ..

5(+7x^2-2x-7x+2)=0

We multiply parentheses

35x^2-10x-35x+10=0

We add all the numbers together, and all the variables

35x^2-45x+10=0

a = 35; b = -45; c = +10;
Δ = b2-4ac
Δ = -452-4·35·10
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{-(-45)-25}{2*35}=\frac{20}{70}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+25}{2*35}=\frac{70}{70}
=1
$