X=2/3x+45

Solution for X=2/3x+45 equation:

X=2/3X+45

We move all terms to the left:

X-(2/3X+45)=0


Domain of the equation: 3X+45)!=0

X∈R


We get rid of parentheses

X-2/3X-45=0

We multiply all the terms by the denominator


X*3X-45*3X-2=0

Wy multiply elements

3X^2-135X-2=0

a = 3; b = -135; c = -2;
Δ = b2-4ac
Δ = -1352-4·3·(-2)
Δ = 18249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-\sqrt{18249}}{2*3}=\frac{135-\sqrt{18249}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18249}}{2*3}=\frac{135+\sqrt{18249}}{6}
$