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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

6x-(5x(-4x+17))-10=0


We calculate terms in parentheses: -(5x(-4x+17)), so:

5x(-4x+17)

We multiply parentheses

-20x^2+85x

Back to the equation:

-(-20x^2+85x)


We get rid of parentheses

20x^2-85x+6x-10=0

We add all the numbers together, and all the variables

20x^2-79x-10=0

a = 20; b = -79; c = -10;
Δ = b2-4ac
Δ = -792-4·20·(-10)
Δ = 7041
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{-(-79)-\sqrt{7041}}{2*20}=\frac{79-\sqrt{7041}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+\sqrt{7041}}{2*20}=\frac{79+\sqrt{7041}}{40}
$