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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-14X^2-33X+5=0

a = -14; b = -33; c = +5;
Δ = b2-4ac
Δ = -332-4·(-14)·5
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-37}{2*-14}=\frac{-4}{-28}
=1/7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+37}{2*-14}=\frac{70}{-28}
=-2+1/2
$