(3x-9)(x+2)=-25x-53

Solution for (3x-9)(x+2)=-25x-53 equation:

(3x-9)(x+2)=-25x-53

We move all terms to the left:

(3x-9)(x+2)-(-25x-53)=0

We get rid of parentheses

(3x-9)(x+2)+25x+53=0

We multiply parentheses ..

(+3x^2+6x-9x-18)+25x+53=0

We get rid of parentheses

3x^2+6x-9x+25x-18+53=0

We add all the numbers together, and all the variables

3x^2+22x+35=0

a = 3; b = 22; c = +35;
Δ = b2-4ac
Δ = 222-4·3·35
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-8}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+8}{2*3}=\frac{-14}{6}
=-2+1/3
$