3/4x=6+5x=120

Solution for 3/4x=6+5x=120 equation:

3/4x=6+5x=120

We move all terms to the left:

3/4x-(6+5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(5x+6)=0

We get rid of parentheses

3/4x-5x-6=0

We multiply all the terms by the denominator


-5x*4x-6*4x+3=0

Wy multiply elements

-20x^2-24x+3=0

a = -20; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·(-20)·3
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{51}}{2*-20}=\frac{24-4\sqrt{51}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{51}}{2*-20}=\frac{24+4\sqrt{51}}{-40}
$