5x(x-6)=4x

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

5x(x-6)=4x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

5x^2-34x=0

a = 5; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·5·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*5}=\frac{68}{10}
=6+4/5
$