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

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

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

We move all terms to the left:

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

We multiply parentheses

7x^2-14x-(4(x-1))=0


We calculate terms in parentheses: -(4(x-1)), so:

4(x-1)

We multiply parentheses

4x-4

Back to the equation:

-(4x-4)


We get rid of parentheses

7x^2-14x-4x+4=0

We add all the numbers together, and all the variables

7x^2-18x+4=0

a = 7; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·7·4
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{53}}{2*7}=\frac{18-2\sqrt{53}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{53}}{2*7}=\frac{18+2\sqrt{53}}{14}
$