9x(x-4)-7x=5(3x-2)

Solution for 9x(x-4)-7x=5(3x-2) equation:

9x(x-4)-7x=5(3x-2)

We move all terms to the left:

9x(x-4)-7x-(5(3x-2))=0

We add all the numbers together, and all the variables

-7x+9x(x-4)-(5(3x-2))=0

We multiply parentheses

9x^2-7x-36x-(5(3x-2))=0


We calculate terms in parentheses: -(5(3x-2)), so:

5(3x-2)

We multiply parentheses

15x-10

Back to the equation:

-(15x-10)


We add all the numbers together, and all the variables

9x^2-43x-(15x-10)=0

We get rid of parentheses

9x^2-43x-15x+10=0

We add all the numbers together, and all the variables

9x^2-58x+10=0

a = 9; b = -58; c = +10;
Δ = b2-4ac
Δ = -582-4·9·10
Δ = 3004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3004}=\sqrt{4*751}=\sqrt{4}*\sqrt{751}=2\sqrt{751}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{751}}{2*9}=\frac{58-2\sqrt{751}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{751}}{2*9}=\frac{58+2\sqrt{751}}{18}
$