5x(x-6)=(4x-5)(x-6)

Solution for 5x(x-6)=(4x-5)(x-6) equation:

5x(x-6)=(4x-5)(x-6)

We move all terms to the left:

5x(x-6)-((4x-5)(x-6))=0

We multiply parentheses

5x^2-30x-((4x-5)(x-6))=0

We multiply parentheses ..

5x^2-((+4x^2-24x-5x+30))-30x=0


We calculate terms in parentheses: -((+4x^2-24x-5x+30)), so:

(+4x^2-24x-5x+30)

We get rid of parentheses

4x^2-24x-5x+30

We add all the numbers together, and all the variables

4x^2-29x+30

Back to the equation:

-(4x^2-29x+30)


We add all the numbers together, and all the variables

5x^2-30x-(4x^2-29x+30)=0

We get rid of parentheses

5x^2-4x^2-30x+29x-30=0

We add all the numbers together, and all the variables

x^2-1x-30=0

a = 1; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·1·(-30)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*1}=\frac{12}{2}
=6
$