x(4x-3)-19=8x-4

Solution for x(4x-3)-19=8x-4 equation:

x(4x-3)-19=8x-4

We move all terms to the left:

x(4x-3)-19-(8x-4)=0

We multiply parentheses

4x^2-3x-(8x-4)-19=0

We get rid of parentheses

4x^2-3x-8x+4-19=0

We add all the numbers together, and all the variables

4x^2-11x-15=0

a = 4; b = -11; c = -15;
Δ = b2-4ac
Δ = -112-4·4·(-15)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-19}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+19}{2*4}=\frac{30}{8}
=3+3/4
$