5x-4=7(2x-1)(x-2)

Solution for 5x-4=7(2x-1)(x-2) equation:

5x-4=7(2x-1)(x-2)

We move all terms to the left:

5x-4-(7(2x-1)(x-2))=0

We multiply parentheses ..

-(7(+2x^2-4x-1x+2))+5x-4=0


We calculate terms in parentheses: -(7(+2x^2-4x-1x+2)), so:

7(+2x^2-4x-1x+2)

We multiply parentheses

14x^2-28x-7x+14

We add all the numbers together, and all the variables

14x^2-35x+14

Back to the equation:

-(14x^2-35x+14)


We add all the numbers together, and all the variables

5x-(14x^2-35x+14)-4=0

We get rid of parentheses

-14x^2+5x+35x-14-4=0

We add all the numbers together, and all the variables

-14x^2+40x-18=0

a = -14; b = 40; c = -18;
Δ = b2-4ac
Δ = 402-4·(-14)·(-18)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{37}}{2*-14}=\frac{-40-4\sqrt{37}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{37}}{2*-14}=\frac{-40+4\sqrt{37}}{-28}
$