x(2x-6)=5(x-1)

Solution for x(2x-6)=5(x-1) equation:

x(2x-6)=5(x-1)

We move all terms to the left:

x(2x-6)-(5(x-1))=0

We multiply parentheses

2x^2-6x-(5(x-1))=0


We calculate terms in parentheses: -(5(x-1)), so:

5(x-1)

We multiply parentheses

5x-5

Back to the equation:

-(5x-5)


We get rid of parentheses

2x^2-6x-5x+5=0

We add all the numbers together, and all the variables

2x^2-11x+5=0

a = 2; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·2·5
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-9}{2*2}=\frac{2}{4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*2}=\frac{20}{4}
=5
$