3.1x+7=1/2x-6

Solution for 3.1x+7=1/2x-6 equation:

3.1x+7=1/2x-6

We move all terms to the left:

3.1x+7-(1/2x-6)=0


Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

3.1x-1/2x+6+7=0

We multiply all the terms by the denominator


(3.1x)*2x+6*2x+7*2x-1=0

We add all the numbers together, and all the variables

(+3.1x)*2x+6*2x+7*2x-1=0

We multiply parentheses

6x^2+6*2x+7*2x-1=0

Wy multiply elements

6x^2+12x+14x-1=0

We add all the numbers together, and all the variables

6x^2+26x-1=0

a = 6; b = 26; c = -1;
Δ = b2-4ac
Δ = 262-4·6·(-1)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-10\sqrt{7}}{2*6}=\frac{-26-10\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+10\sqrt{7}}{2*6}=\frac{-26+10\sqrt{7}}{12}
$