(-2/3)(15x+3)=-3x-9

Solution for (-2/3)(15x+3)=-3x-9 equation:

(-2/3)(15x+3)=-3x-9

We move all terms to the left:

(-2/3)(15x+3)-(-3x-9)=0


Domain of the equation: 3)(15x+3)!=0

x∈R


We get rid of parentheses

(-2/3)(15x+3)+3x+9=0

We multiply parentheses ..

(-30x^2-2/3*3)+3x+9=0

We multiply all the terms by the denominator


(-30x^2-2+3x*3*3)+9*3*3)=0

We add all the numbers together, and all the variables

(-30x^2-2+3x*3*3)=0

We get rid of parentheses

-30x^2+3x*3*3-2=0

Wy multiply elements

-30x^2+27x*3-2=0

Wy multiply elements

-30x^2+81x-2=0

a = -30; b = 81; c = -2;
Δ = b2-4ac
Δ = 812-4·(-30)·(-2)
Δ = 6321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6321}=\sqrt{49*129}=\sqrt{49}*\sqrt{129}=7\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-7\sqrt{129}}{2*-30}=\frac{-81-7\sqrt{129}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+7\sqrt{129}}{2*-30}=\frac{-81+7\sqrt{129}}{-60}
$