9x-16=3x(x-5)

Solution for 9x-16=3x(x-5) equation:

9x-16=3x(x-5)

We move all terms to the left:

9x-16-(3x(x-5))=0


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

3x(x-5)

We multiply parentheses

3x^2-15x

Back to the equation:

-(3x^2-15x)


We get rid of parentheses

-3x^2+9x+15x-16=0

We add all the numbers together, and all the variables

-3x^2+24x-16=0

a = -3; b = 24; c = -16;
Δ = b2-4ac
Δ = 242-4·(-3)·(-16)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{6}}{2*-3}=\frac{-24-8\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{6}}{2*-3}=\frac{-24+8\sqrt{6}}{-6}
$