5x+2=1/2*2x+36

Solution for 5x+2=1/2*2x+36 equation:

5x+2=1/2*2x+36

We move all terms to the left:

5x+2-(1/2*2x+36)=0


Domain of the equation: 2*2x+36)!=0

x∈R


We get rid of parentheses

5x-1/2*2x-36+2=0

We multiply all the terms by the denominator


5x*2*2x-36*2*2x+2*2*2x-1=0

Wy multiply elements

20x^2*2-144x*2+8x*2-1=0

Wy multiply elements

40x^2-288x+16x-1=0

We add all the numbers together, and all the variables

40x^2-272x-1=0

a = 40; b = -272; c = -1;
Δ = b2-4ac
Δ = -2722-4·40·(-1)
Δ = 74144
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:

$\sqrt{\Delta}=\sqrt{74144}=\sqrt{16*4634}=\sqrt{16}*\sqrt{4634}=4\sqrt{4634}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-272)-4\sqrt{4634}}{2*40}=\frac{272-4\sqrt{4634}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-272)+4\sqrt{4634}}{2*40}=\frac{272+4\sqrt{4634}}{80}
$