X+402/3x=180

Solution for X+402/3x=180 equation:

X+402/3X=180

We move all terms to the left:

X+402/3X-(180)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-180*3X+402=0

Wy multiply elements

3X^2-540X+402=0

a = 3; b = -540; c = +402;
Δ = b2-4ac
Δ = -5402-4·3·402
Δ = 286776
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:

$\sqrt{\Delta}=\sqrt{286776}=\sqrt{36*7966}=\sqrt{36}*\sqrt{7966}=6\sqrt{7966}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-6\sqrt{7966}}{2*3}=\frac{540-6\sqrt{7966}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+6\sqrt{7966}}{2*3}=\frac{540+6\sqrt{7966}}{6}
$