-5x(x+2)=3(x+2)-20

Solution for -5x(x+2)=3(x+2)-20 equation:

-5x(x+2)=3(x+2)-20

We move all terms to the left:

-5x(x+2)-(3(x+2)-20)=0

We multiply parentheses

-5x^2-10x-(3(x+2)-20)=0


We calculate terms in parentheses: -(3(x+2)-20), so:

3(x+2)-20

We multiply parentheses

3x+6-20

We add all the numbers together, and all the variables

3x-14

Back to the equation:

-(3x-14)


We get rid of parentheses

-5x^2-10x-3x+14=0

We add all the numbers together, and all the variables

-5x^2-13x+14=0

a = -5; b = -13; c = +14;
Δ = b2-4ac
Δ = -132-4·(-5)·14
Δ = 449
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{-(-13)-\sqrt{449}}{2*-5}=\frac{13-\sqrt{449}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{449}}{2*-5}=\frac{13+\sqrt{449}}{-10}
$