-19+3x=3x(x-5)

Solution for -19+3x=3x(x-5) equation:

-19+3x=3x(x-5)

We move all terms to the left:

-19+3x-(3x(x-5))=0


We calculate terms in parentheses: -(3x(x-5)), so:

3x(x-5)

We multiply parentheses

3x^2-15x

Back to the equation:

-(3x^2-15x)


We get rid of parentheses

-3x^2+3x+15x-19=0

We add all the numbers together, and all the variables

-3x^2+18x-19=0

a = -3; b = 18; c = -19;
Δ = b2-4ac
Δ = 182-4·(-3)·(-19)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{6}}{2*-3}=\frac{-18-4\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{6}}{2*-3}=\frac{-18+4\sqrt{6}}{-6}
$