(4x-1)(x-2)=7x-2

Solution for (4x-1)(x-2)=7x-2 equation:

(4x-1)(x-2)=7x-2

We move all terms to the left:

(4x-1)(x-2)-(7x-2)=0

We get rid of parentheses

(4x-1)(x-2)-7x+2=0

We multiply parentheses ..

(+4x^2-8x-1x+2)-7x+2=0

We get rid of parentheses

4x^2-8x-1x-7x+2+2=0

We add all the numbers together, and all the variables

4x^2-16x+4=0

a = 4; b = -16; c = +4;
Δ = b2-4ac
Δ = -162-4·4·4
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{3}}{2*4}=\frac{16-8\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{3}}{2*4}=\frac{16+8\sqrt{3}}{8}
$