0.75x+40=11/3x

Solution for 0.75x+40=11/3x equation:

0.75x+40=11/3x

We move all terms to the left:

0.75x+40-(11/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.75x-(+11/3x)+40=0

We get rid of parentheses

0.75x-11/3x+40=0

We multiply all the terms by the denominator


(0.75x)*3x+40*3x-11=0

We add all the numbers together, and all the variables

(+0.75x)*3x+40*3x-11=0

We multiply parentheses

0x^2+40*3x-11=0

Wy multiply elements

0x^2+120x-11=0

We add all the numbers together, and all the variables

x^2+120x-11=0

a = 1; b = 120; c = -11;
Δ = b2-4ac
Δ = 1202-4·1·(-11)
Δ = 14444
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:

$\sqrt{\Delta}=\sqrt{14444}=\sqrt{4*3611}=\sqrt{4}*\sqrt{3611}=2\sqrt{3611}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3611}}{2*1}=\frac{-120-2\sqrt{3611}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3611}}{2*1}=\frac{-120+2\sqrt{3611}}{2}
$