2x+4(x-1)=1/2x-9

Solution for 2x+4(x-1)=1/2x-9 equation:

2x+4(x-1)=1/2x-9

We move all terms to the left:

2x+4(x-1)-(1/2x-9)=0


Domain of the equation: 2x-9)!=0

x∈R


We multiply parentheses

2x+4x-(1/2x-9)-4=0

We get rid of parentheses

2x+4x-1/2x+9-4=0

We multiply all the terms by the denominator


2x*2x+4x*2x+9*2x-4*2x-1=0

Wy multiply elements

4x^2+8x^2+18x-8x-1=0

We add all the numbers together, and all the variables

12x^2+10x-1=0

a = 12; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·12·(-1)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{37}}{2*12}=\frac{-10-2\sqrt{37}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{37}}{2*12}=\frac{-10+2\sqrt{37}}{24}
$