2/7x-12=3x-16

Solution for 2/7x-12=3x-16 equation:

2/7x-12=3x-16

We move all terms to the left:

2/7x-12-(3x-16)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

2/7x-3x+16-12=0

We multiply all the terms by the denominator


-3x*7x+16*7x-12*7x+2=0

Wy multiply elements

-21x^2+112x-84x+2=0

We add all the numbers together, and all the variables

-21x^2+28x+2=0

a = -21; b = 28; c = +2;
Δ = b2-4ac
Δ = 282-4·(-21)·2
Δ = 952
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:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{238}}{2*-21}=\frac{-28-2\sqrt{238}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{238}}{2*-21}=\frac{-28+2\sqrt{238}}{-42}
$