3x-19=4x(2x-17)

Solution for 3x-19=4x(2x-17) equation:

3x-19=4x(2x-17)

We move all terms to the left:

3x-19-(4x(2x-17))=0


We calculate terms in parentheses: -(4x(2x-17)), so:

4x(2x-17)

We multiply parentheses

8x^2-68x

Back to the equation:

-(8x^2-68x)


We get rid of parentheses

-8x^2+3x+68x-19=0

We add all the numbers together, and all the variables

-8x^2+71x-19=0

a = -8; b = 71; c = -19;
Δ = b2-4ac
Δ = 712-4·(-8)·(-19)
Δ = 4433
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(71)-\sqrt{4433}}{2*-8}=\frac{-71-\sqrt{4433}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(71)+\sqrt{4433}}{2*-8}=\frac{-71+\sqrt{4433}}{-16}
$