4x=5x(x-38)

Solution for 4x=5x(x-38) equation:

4x=5x(x-38)

We move all terms to the left:

4x-(5x(x-38))=0


We calculate terms in parentheses: -(5x(x-38)), so:

5x(x-38)

We multiply parentheses

5x^2-190x

Back to the equation:

-(5x^2-190x)


We get rid of parentheses

-5x^2+4x+190x=0

We add all the numbers together, and all the variables

-5x^2+194x=0

a = -5; b = 194; c = 0;
Δ = b2-4ac
Δ = 1942-4·(-5)·0
Δ = 37636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{37636}=194$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(194)-194}{2*-5}=\frac{-388}{-10}
=38+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(194)+194}{2*-5}=\frac{0}{-10}
=0
$