(3/4)x-12=-3x+13

Solution for (3/4)x-12=-3x+13 equation:

(3/4)x-12=-3x+13

We move all terms to the left:

(3/4)x-12-(-3x+13)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)x-(-3x+13)-12=0

We multiply parentheses

3x^2-(-3x+13)-12=0

We get rid of parentheses

3x^2+3x-13-12=0

We add all the numbers together, and all the variables

3x^2+3x-25=0

a = 3; b = 3; c = -25;
Δ = b2-4ac
Δ = 32-4·3·(-25)
Δ = 309
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{-(3)-\sqrt{309}}{2*3}=\frac{-3-\sqrt{309}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{309}}{2*3}=\frac{-3+\sqrt{309}}{6}
$