5x-6=45-2/3x

Solution for 5x-6=45-2/3x equation:

5x-6=45-2/3x

We move all terms to the left:

5x-6-(45-2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(-2/3x+45)-6=0

We get rid of parentheses

5x+2/3x-45-6=0

We multiply all the terms by the denominator


5x*3x-45*3x-6*3x+2=0

Wy multiply elements

15x^2-135x-18x+2=0

We add all the numbers together, and all the variables

15x^2-153x+2=0

a = 15; b = -153; c = +2;
Δ = b2-4ac
Δ = -1532-4·15·2
Δ = 23289
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{-(-153)-\sqrt{23289}}{2*15}=\frac{153-\sqrt{23289}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-153)+\sqrt{23289}}{2*15}=\frac{153+\sqrt{23289}}{30}
$