(6x)=16-12/2(6x)+3

Solution for (6x)=16-12/2(6x)+3 equation:

(6x)=16-12/2(6x)+3

We move all terms to the left:

(6x)-(16-12/2(6x)+3)=0


Domain of the equation: 26x+3)!=0

x∈R


We add all the numbers together, and all the variables

6x-(-12/26x+19)=0

We get rid of parentheses

6x+12/26x-19=0

We multiply all the terms by the denominator


6x*26x-19*26x+12=0

Wy multiply elements

156x^2-494x+12=0

a = 156; b = -494; c = +12;
Δ = b2-4ac
Δ = -4942-4·156·12
Δ = 236548
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:

$\sqrt{\Delta}=\sqrt{236548}=\sqrt{4*59137}=\sqrt{4}*\sqrt{59137}=2\sqrt{59137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-494)-2\sqrt{59137}}{2*156}=\frac{494-2\sqrt{59137}}{312}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-494)+2\sqrt{59137}}{2*156}=\frac{494+2\sqrt{59137}}{312}
$