8(x^2-14/3X)=32

Solution for 8(x^2-14/3X)=32 equation:

8(x^2-14/3x)=32

We move all terms to the left:

8(x^2-14/3x)-(32)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We multiply parentheses

8x^2-112x-32=0

a = 8; b = -112; c = -32;
Δ = b2-4ac
Δ = -1122-4·8·(-32)
Δ = 13568
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:

$\sqrt{\Delta}=\sqrt{13568}=\sqrt{256*53}=\sqrt{256}*\sqrt{53}=16\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-16\sqrt{53}}{2*8}=\frac{112-16\sqrt{53}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+16\sqrt{53}}{2*8}=\frac{112+16\sqrt{53}}{16}
$