3X+3=1/2x+13

Solution for 3X+3=1/2x+13 equation:

3X+3=1/2X+13

We move all terms to the left:

3X+3-(1/2X+13)=0


Domain of the equation: 2X+13)!=0

X∈R


We get rid of parentheses

3X-1/2X-13+3=0

We multiply all the terms by the denominator


3X*2X-13*2X+3*2X-1=0

Wy multiply elements

6X^2-26X+6X-1=0

We add all the numbers together, and all the variables

6X^2-20X-1=0

a = 6; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·6·(-1)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{106}}{2*6}=\frac{20-2\sqrt{106}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{106}}{2*6}=\frac{20+2\sqrt{106}}{12}
$