3x+6^1/2=5/2x+5

Solution for 3x+6^1/2=5/2x+5 equation:

3x+6^1/2=5/2x+5

We move all terms to the left:

3x+6^1/2-(5/2x+5)=0


Domain of the equation: 2x+5)!=0

x∈R


We add all the numbers together, and all the variables

3x-(5/2x+5)+3=0

We get rid of parentheses

3x-5/2x-5+3=0

We multiply all the terms by the denominator


3x*2x-5*2x+3*2x-5=0

Wy multiply elements

6x^2-10x+6x-5=0

We add all the numbers together, and all the variables

6x^2-4x-5=0

a = 6; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·6·(-5)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{34}}{2*6}=\frac{4-2\sqrt{34}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{34}}{2*6}=\frac{4+2\sqrt{34}}{12}
$