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-8)!=0

X∈R


We get rid of parentheses

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 = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{123}}{2*3}=\frac{-24-2\sqrt{123}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{123}}{2*3}=\frac{-24+2\sqrt{123}}{6}
$