2/3)9+x)=-5(4-x)

Solution for 2/3)9+x)=-5(4-x) equation:

2/3)9+x)=-5(4-x)

We move all terms to the left:

2/3)9+x)-(-5(4-x))=0


Domain of the equation: 3)9+x)-(-5(4!=0

x∈R


We add all the numbers together, and all the variables

2/3)9+x)-(-5(-1x+4))=0

We add all the numbers together, and all the variables

-1x+2/3)9+x)-(-5(=0

We multiply all the terms by the denominator


-1x*3)9+x)-(-5(+2=0

Wy multiply elements

-3x^2+2=0

a = -3; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-3)·2
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*-3}=\frac{0-2\sqrt{6}}{-6}
=-\frac{2\sqrt{6}}{-6}
=-\frac{\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*-3}=\frac{0+2\sqrt{6}}{-6}
=\frac{2\sqrt{6}}{-6}
=\frac{\sqrt{6}}{-3}
$