x+(8/11x)=76

Solution for x+(8/11x)=76 equation:

x+(8/11x)=76

We move all terms to the left:

x+(8/11x)-(76)=0


Domain of the equation: 11x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+8/11x)-76=0

We get rid of parentheses

x+8/11x-76=0

We multiply all the terms by the denominator


x*11x-76*11x+8=0

Wy multiply elements

11x^2-836x+8=0

a = 11; b = -836; c = +8;
Δ = b2-4ac
Δ = -8362-4·11·8
Δ = 698544
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:

$\sqrt{\Delta}=\sqrt{698544}=\sqrt{63504*11}=\sqrt{63504}*\sqrt{11}=252\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-836)-252\sqrt{11}}{2*11}=\frac{836-252\sqrt{11}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-836)+252\sqrt{11}}{2*11}=\frac{836+252\sqrt{11}}{22}
$