3(x-3)-16=2x(x-8)+11

Solution for 3(x-3)-16=2x(x-8)+11 equation:

3(x-3)-16=2x(x-8)+11

We move all terms to the left:

3(x-3)-16-(2x(x-8)+11)=0

We multiply parentheses

3x-(2x(x-8)+11)-9-16=0


We calculate terms in parentheses: -(2x(x-8)+11), so:

2x(x-8)+11

We multiply parentheses

2x^2-16x+11

Back to the equation:

-(2x^2-16x+11)


We add all the numbers together, and all the variables

3x-(2x^2-16x+11)-25=0

We get rid of parentheses

-2x^2+3x+16x-11-25=0

We add all the numbers together, and all the variables

-2x^2+19x-36=0

a = -2; b = 19; c = -36;
Δ = b2-4ac
Δ = 192-4·(-2)·(-36)
Δ = 73
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{-(19)-\sqrt{73}}{2*-2}=\frac{-19-\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{73}}{2*-2}=\frac{-19+\sqrt{73}}{-4}
$