1-6x=-3/2x+7

Solution for 1-6x=-3/2x+7 equation:

1-6x=-3/2x+7

We move all terms to the left:

1-6x-(-3/2x+7)=0


Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

-6x+3/2x-7+1=0

We multiply all the terms by the denominator


-6x*2x-7*2x+1*2x+3=0

Wy multiply elements

-12x^2-14x+2x+3=0

We add all the numbers together, and all the variables

-12x^2-12x+3=0

a = -12; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·(-12)·3
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*-12}=\frac{12-12\sqrt{2}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*-12}=\frac{12+12\sqrt{2}}{-24}
$