4x-12/3x+21=-7

Solution for 4x-12/3x+21=-7 equation:

4x-12/3x+21=-7

We move all terms to the left:

4x-12/3x+21-(-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x-12/3x+28=0

We multiply all the terms by the denominator


4x*3x+28*3x-12=0

Wy multiply elements

12x^2+84x-12=0

a = 12; b = 84; c = -12;
Δ = b2-4ac
Δ = 842-4·12·(-12)
Δ = 7632
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:

$\sqrt{\Delta}=\sqrt{7632}=\sqrt{144*53}=\sqrt{144}*\sqrt{53}=12\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-12\sqrt{53}}{2*12}=\frac{-84-12\sqrt{53}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12\sqrt{53}}{2*12}=\frac{-84+12\sqrt{53}}{24}
$