-3x(x+4)+4=5(x+3)+6

Solution for -3x(x+4)+4=5(x+3)+6 equation:

-3x(x+4)+4=5(x+3)+6

We move all terms to the left:

-3x(x+4)+4-(5(x+3)+6)=0

We multiply parentheses

-3x^2-12x-(5(x+3)+6)+4=0


We calculate terms in parentheses: -(5(x+3)+6), so:

5(x+3)+6

We multiply parentheses

5x+15+6

We add all the numbers together, and all the variables

5x+21

Back to the equation:

-(5x+21)


We get rid of parentheses

-3x^2-12x-5x-21+4=0

We add all the numbers together, and all the variables

-3x^2-17x-17=0

a = -3; b = -17; c = -17;
Δ = b2-4ac
Δ = -172-4·(-3)·(-17)
Δ = 85
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{-(-17)-\sqrt{85}}{2*-3}=\frac{17-\sqrt{85}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{85}}{2*-3}=\frac{17+\sqrt{85}}{-6}
$