3/11x+2=5x-102

Solution for 3/11x+2=5x-102 equation:

3/11x+2=5x-102

We move all terms to the left:

3/11x+2-(5x-102)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We get rid of parentheses

3/11x-5x+102+2=0

We multiply all the terms by the denominator


-5x*11x+102*11x+2*11x+3=0

Wy multiply elements

-55x^2+1122x+22x+3=0

We add all the numbers together, and all the variables

-55x^2+1144x+3=0

a = -55; b = 1144; c = +3;
Δ = b2-4ac
Δ = 11442-4·(-55)·3
Δ = 1309396
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:

$\sqrt{\Delta}=\sqrt{1309396}=\sqrt{4*327349}=\sqrt{4}*\sqrt{327349}=2\sqrt{327349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1144)-2\sqrt{327349}}{2*-55}=\frac{-1144-2\sqrt{327349}}{-110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1144)+2\sqrt{327349}}{2*-55}=\frac{-1144+2\sqrt{327349}}{-110}
$