5x+12/6x+3=180

Solution for 5x+12/6x+3=180 equation:

5x+12/6x+3=180

We move all terms to the left:

5x+12/6x+3-(180)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

5x+12/6x-177=0

We multiply all the terms by the denominator


5x*6x-177*6x+12=0

Wy multiply elements

30x^2-1062x+12=0

a = 30; b = -1062; c = +12;
Δ = b2-4ac
Δ = -10622-4·30·12
Δ = 1126404
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:

$\sqrt{\Delta}=\sqrt{1126404}=\sqrt{36*31289}=\sqrt{36}*\sqrt{31289}=6\sqrt{31289}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1062)-6\sqrt{31289}}{2*30}=\frac{1062-6\sqrt{31289}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1062)+6\sqrt{31289}}{2*30}=\frac{1062+6\sqrt{31289}}{60}
$