5/3X+3=x+7

Solution for 5/3X+3=x+7 equation:

5/3X+3=X+7

We move all terms to the left:

5/3X+3-(X+7)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We get rid of parentheses

5/3X-X-7+3=0

We multiply all the terms by the denominator


-X*3X-7*3X+3*3X+5=0

Wy multiply elements

-3X^2-21X+9X+5=0

We add all the numbers together, and all the variables

-3X^2-12X+5=0

a = -3; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·(-3)·5
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{51}}{2*-3}=\frac{12-2\sqrt{51}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{51}}{2*-3}=\frac{12+2\sqrt{51}}{-6}
$