(4/3)x-(11/3)=-4x+37

Solution for (4/3)x-(11/3)=-4x+37 equation:

(4/3)x-(11/3)=-4x+37

We move all terms to the left:

(4/3)x-(11/3)-(-4x+37)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/3)x-(-4x+37)-(+11/3)=0

We multiply parentheses

4x^2-(-4x+37)-(+11/3)=0

We get rid of parentheses

4x^2+4x-37-11/3=0

We multiply all the terms by the denominator


4x^2*3+4x*3-11-37*3=0

We add all the numbers together, and all the variables

4x^2*3+4x*3-122=0

Wy multiply elements

12x^2+12x-122=0

a = 12; b = 12; c = -122;
Δ = b2-4ac
Δ = 122-4·12·(-122)
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20\sqrt{15}}{2*12}=\frac{-12-20\sqrt{15}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20\sqrt{15}}{2*12}=\frac{-12+20\sqrt{15}}{24}
$