9x-5=3x(x-2)+13

Solution for 9x-5=3x(x-2)+13 equation:

9x-5=3x(x-2)+13

We move all terms to the left:

9x-5-(3x(x-2)+13)=0


We calculate terms in parentheses: -(3x(x-2)+13), so:

3x(x-2)+13

We multiply parentheses

3x^2-6x+13

Back to the equation:

-(3x^2-6x+13)


We get rid of parentheses

-3x^2+9x+6x-13-5=0

We add all the numbers together, and all the variables

-3x^2+15x-18=0

a = -3; b = 15; c = -18;
Δ = b2-4ac
Δ = 152-4·(-3)·(-18)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*-3}=\frac{-12}{-6}
=+2
$