(5/2)X-12=3x+6

Solution for (5/2)X-12=3x+6 equation:

(5/2)X-12=3X+6

We move all terms to the left:

(5/2)X-12-(3X+6)=0


Domain of the equation: 2)X!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(+5/2)X-(3X+6)-12=0

We multiply parentheses

5X^2-(3X+6)-12=0

We get rid of parentheses

5X^2-3X-6-12=0

We add all the numbers together, and all the variables

5X^2-3X-18=0

a = 5; b = -3; c = -18;
Δ = b2-4ac
Δ = -32-4·5·(-18)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{41}}{2*5}=\frac{3-3\sqrt{41}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{41}}{2*5}=\frac{3+3\sqrt{41}}{10}
$