(1/2x+17)=4x+2

Solution for (1/2x+17)=4x+2 equation:

(1/2x+17)=4x+2

We move all terms to the left:

(1/2x+17)-(4x+2)=0


Domain of the equation: 2x+17)!=0

x∈R


We get rid of parentheses

1/2x-4x+17-2=0

We multiply all the terms by the denominator


-4x*2x+17*2x-2*2x+1=0

Wy multiply elements

-8x^2+34x-4x+1=0

We add all the numbers together, and all the variables

-8x^2+30x+1=0

a = -8; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·(-8)·1
Δ = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{233}}{2*-8}=\frac{-30-2\sqrt{233}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{233}}{2*-8}=\frac{-30+2\sqrt{233}}{-16}
$