5x-17=3x(x-3)+2x(x-4)

Solution for 5x-17=3x(x-3)+2x(x-4) equation:

5x-17=3x(x-3)+2x(x-4)

We move all terms to the left:

5x-17-(3x(x-3)+2x(x-4))=0


We calculate terms in parentheses: -(3x(x-3)+2x(x-4)), so:

3x(x-3)+2x(x-4)

We multiply parentheses

3x^2+2x^2-9x-8x

We add all the numbers together, and all the variables

5x^2-17x

Back to the equation:

-(5x^2-17x)


We get rid of parentheses

-5x^2+5x+17x-17=0

We add all the numbers together, and all the variables

-5x^2+22x-17=0

a = -5; b = 22; c = -17;
Δ = b2-4ac
Δ = 222-4·(-5)·(-17)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-12}{2*-5}=\frac{-34}{-10}
=3+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+12}{2*-5}=\frac{-10}{-10}
=1
$