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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2-15x-19x+95)-(3(x-3))=0


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

3(x-3)

We multiply parentheses

3x-9

Back to the equation:

-(3x-9)


We get rid of parentheses

3x^2-15x-19x-3x+95+9=0

We add all the numbers together, and all the variables

3x^2-37x+104=0

a = 3; b = -37; c = +104;
Δ = b2-4ac
Δ = -372-4·3·104
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{-(-37)-11}{2*3}=\frac{26}{6}
=4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+11}{2*3}=\frac{48}{6}
=8
$