1/2x-4=-3x+11

Solution for 1/2x-4=-3x+11 equation:

1/2x-4=-3x+11

We move all terms to the left:

1/2x-4-(-3x+11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+3x-11-4=0

We multiply all the terms by the denominator


3x*2x-11*2x-4*2x+1=0

Wy multiply elements

6x^2-22x-8x+1=0

We add all the numbers together, and all the variables

6x^2-30x+1=0

a = 6; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·6·1
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*6}=\frac{30-2\sqrt{219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*6}=\frac{30+2\sqrt{219}}{12}
$