8x+5(4/3)x=22

Solution for 8x+5(4/3)x=22 equation:

8x+5(4/3)x=22

We move all terms to the left:

8x+5(4/3)x-(22)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x+5(+4/3)x-22=0

We multiply parentheses

20x^2+8x-22=0

a = 20; b = 8; c = -22;
Δ = b2-4ac
Δ = 82-4·20·(-22)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{114}}{2*20}=\frac{-8-4\sqrt{114}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{114}}{2*20}=\frac{-8+4\sqrt{114}}{40}
$