(-3x-5)(2x-1)=0

Solution for (-3x-5)(2x-1)=0 equation:

(-3x-5)(2x-1)=0

We multiply parentheses ..

(-6x^2+3x-10x+5)=0

We get rid of parentheses

-6x^2+3x-10x+5=0

We add all the numbers together, and all the variables

-6x^2-7x+5=0

a = -6; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·(-6)·5
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-6}=\frac{-6}{-12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-6}=\frac{20}{-12}
=-1+2/3
$