4(x+3)-4=81/2x+1

Solution for 4(x+3)-4=81/2x+1 equation:

4(x+3)-4=81/2x+1

We move all terms to the left:

4(x+3)-4-(81/2x+1)=0


Domain of the equation: 2x+1)!=0

x∈R


We multiply parentheses

4x-(81/2x+1)+12-4=0

We get rid of parentheses

4x-81/2x-1+12-4=0

We multiply all the terms by the denominator


4x*2x-1*2x+12*2x-4*2x-81=0

Wy multiply elements

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

We add all the numbers together, and all the variables

8x^2+14x-81=0

a = 8; b = 14; c = -81;
Δ = b2-4ac
Δ = 142-4·8·(-81)
Δ = 2788
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:

$\sqrt{\Delta}=\sqrt{2788}=\sqrt{4*697}=\sqrt{4}*\sqrt{697}=2\sqrt{697}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{697}}{2*8}=\frac{-14-2\sqrt{697}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{697}}{2*8}=\frac{-14+2\sqrt{697}}{16}
$