3/2x-2=-x+13

Solution for 3/2x-2=-x+13 equation:

3/2x-2=-x+13

We move all terms to the left:

3/2x-2-(-x+13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(-1x+13)-2=0

We get rid of parentheses

3/2x+1x-13-2=0

We multiply all the terms by the denominator


1x*2x-13*2x-2*2x+3=0

Wy multiply elements

2x^2-26x-4x+3=0

We add all the numbers together, and all the variables

2x^2-30x+3=0

a = 2; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·2·3
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*2}=\frac{30-2\sqrt{219}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*2}=\frac{30+2\sqrt{219}}{4}
$