X-7=-10/3x+6

Solution for X-7=-10/3x+6 equation:

X-7=-10/3X+6

We move all terms to the left:

X-7-(-10/3X+6)=0


Domain of the equation: 3X+6)!=0

X∈R


We get rid of parentheses

X+10/3X-6-7=0

We multiply all the terms by the denominator


X*3X-6*3X-7*3X+10=0

Wy multiply elements

3X^2-18X-21X+10=0

We add all the numbers together, and all the variables

3X^2-39X+10=0

a = 3; b = -39; c = +10;
Δ = b2-4ac
Δ = -392-4·3·10
Δ = 1401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1401}}{2*3}=\frac{39-\sqrt{1401}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1401}}{2*3}=\frac{39+\sqrt{1401}}{6}
$