5x+6=3/2x

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

5x+6=3/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5x-3/2x+6=0

We multiply all the terms by the denominator


5x*2x+6*2x-3=0

Wy multiply elements

10x^2+12x-3=0

a = 10; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·10·(-3)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{66}}{2*10}=\frac{-12-2\sqrt{66}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{66}}{2*10}=\frac{-12+2\sqrt{66}}{20}
$