-3/2x+1=x+7

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

-3/2x+1=x+7

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·(-2)·(-3)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*-2}=\frac{12-2\sqrt{30}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*-2}=\frac{12+2\sqrt{30}}{-4}
$