X-7/3x=-8

Solution for X-7/3x=-8 equation:

X-7/3X=-8

We move all terms to the left:

X-7/3X-(-8)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-7/3X+8=0

We multiply all the terms by the denominator


X*3X+8*3X-7=0

Wy multiply elements

3X^2+24X-7=0

a = 3; b = 24; c = -7;
Δ = b2-4ac
Δ = 242-4·3·(-7)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{165}}{2*3}=\frac{-24-2\sqrt{165}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{165}}{2*3}=\frac{-24+2\sqrt{165}}{6}
$