(5x-1)(2x-1)=13

Solution for (5x-1)(2x-1)=13 equation:

(5x-1)(2x-1)=13

We move all terms to the left:

(5x-1)(2x-1)-(13)=0

We multiply parentheses ..

(+10x^2-5x-2x+1)-13=0

We get rid of parentheses

10x^2-5x-2x+1-13=0

We add all the numbers together, and all the variables

10x^2-7x-12=0

a = 10; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·10·(-12)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-23}{2*10}=\frac{-16}{20}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*10}=\frac{30}{20}
=1+1/2
$