4(x-3)-4=81/2x+11

Solution for 4(x-3)-4=81/2x+11 equation:

4(x-3)-4=81/2x+11

We move all terms to the left:

4(x-3)-4-(81/2x+11)=0


Domain of the equation: 2x+11)!=0

x∈R


We multiply parentheses

4x-(81/2x+11)-12-4=0

We get rid of parentheses

4x-81/2x-11-12-4=0

We multiply all the terms by the denominator


4x*2x-11*2x-12*2x-4*2x-81=0

Wy multiply elements

8x^2-22x-24x-8x-81=0

We add all the numbers together, and all the variables

8x^2-54x-81=0

a = 8; b = -54; c = -81;
Δ = b2-4ac
Δ = -542-4·8·(-81)
Δ = 5508
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:

$\sqrt{\Delta}=\sqrt{5508}=\sqrt{324*17}=\sqrt{324}*\sqrt{17}=18\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-18\sqrt{17}}{2*8}=\frac{54-18\sqrt{17}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+18\sqrt{17}}{2*8}=\frac{54+18\sqrt{17}}{16}
$