(2x-1)(3x-5)-4(1-2x)=0

Solution for (2x-1)(3x-5)-4(1-2x)=0 equation:

(2x-1)(3x-5)-4(1-2x)=0

We add all the numbers together, and all the variables

(2x-1)(3x-5)-4(-2x+1)=0

We multiply parentheses

(2x-1)(3x-5)+8x-4=0

We multiply parentheses ..

(+6x^2-10x-3x+5)+8x-4=0

We get rid of parentheses

6x^2-10x-3x+8x+5-4=0

We add all the numbers together, and all the variables

6x^2-5x+1=0

a = 6; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·6·1
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*6}=\frac{4}{12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*6}=\frac{6}{12}
=1/2
$