x+(2/3)*x+(4/9)*x=76

Solution for x+(2/3)*x+(4/9)*x=76 equation:

x+(2/3)*x+(4/9)*x=76

We move all terms to the left:

x+(2/3)*x+(4/9)*x-(76)=0


Domain of the equation: 3)*x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 9)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+2/3)*x+(+4/9)*x-76=0

We multiply parentheses

2x^2+4x^2+x-76=0

We add all the numbers together, and all the variables

6x^2+x-76=0

a = 6; b = 1; c = -76;
Δ = b2-4ac
Δ = 12-4·6·(-76)
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{73}}{2*6}=\frac{-1-5\sqrt{73}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{73}}{2*6}=\frac{-1+5\sqrt{73}}{12}
$