5x+3/2x+6=0

Solution for 5x+3/2x+6=0 equation:

5x+3/2x+6=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


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 = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{6}}{2*10}=\frac{-12-2\sqrt{6}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{6}}{2*10}=\frac{-12+2\sqrt{6}}{20}
$