3(x+2)+9=-5x(x-8)-3

Solution for 3(x+2)+9=-5x(x-8)-3 equation:

3(x+2)+9=-5x(x-8)-3

We move all terms to the left:

3(x+2)+9-(-5x(x-8)-3)=0

We multiply parentheses

3x-(-5x(x-8)-3)+6+9=0


We calculate terms in parentheses: -(-5x(x-8)-3), so:

-5x(x-8)-3

We multiply parentheses

-5x^2+40x-3

Back to the equation:

-(-5x^2+40x-3)


We add all the numbers together, and all the variables

-(-5x^2+40x-3)+3x+15=0

We get rid of parentheses

5x^2-40x+3x+3+15=0

We add all the numbers together, and all the variables

5x^2-37x+18=0

a = 5; b = -37; c = +18;
Δ = b2-4ac
Δ = -372-4·5·18
Δ = 1009
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{-(-37)-\sqrt{1009}}{2*5}=\frac{37-\sqrt{1009}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1009}}{2*5}=\frac{37+\sqrt{1009}}{10}
$