(2/9)x+(1/4)x=34

Solution for (2/9)x+(1/4)x=34 equation:

(2/9)x+(1/4)x=34

We move all terms to the left:

(2/9)x+(1/4)x-(34)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/9)x+(+1/4)x-34=0

We multiply parentheses

2x^2+x^2-34=0

We add all the numbers together, and all the variables

3x^2-34=0

a = 3; b = 0; c = -34;
Δ = b2-4ac
Δ = 02-4·3·(-34)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{102}}{2*3}=\frac{0-2\sqrt{102}}{6}
=-\frac{2\sqrt{102}}{6}
=-\frac{\sqrt{102}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{102}}{2*3}=\frac{0+2\sqrt{102}}{6}
=\frac{2\sqrt{102}}{6}
=\frac{\sqrt{102}}{3}
$