3/2x+4=x-7

Solution for 3/2x+4=x-7 equation:

3/2x+4=x-7

We move all terms to the left:

3/2x+4-(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+4=0

We multiply all the terms by the denominator


-x*2x+7*2x+4*2x+3=0

Wy multiply elements

-2x^2+14x+8x+3=0

We add all the numbers together, and all the variables

-2x^2+22x+3=0

a = -2; b = 22; c = +3;
Δ = b2-4ac
Δ = 222-4·(-2)·3
Δ = 508
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:

$\sqrt{\Delta}=\sqrt{508}=\sqrt{4*127}=\sqrt{4}*\sqrt{127}=2\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{127}}{2*-2}=\frac{-22-2\sqrt{127}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{127}}{2*-2}=\frac{-22+2\sqrt{127}}{-4}
$