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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

10x^2-17x+3=0

a = 10; b = -17; c = +3;
Δ = b2-4ac
Δ = -172-4·10·3
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{-(-17)-13}{2*10}=\frac{4}{20}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*10}=\frac{30}{20}
=1+1/2
$