7/11x+x=90

Solution for 7/11x+x=90 equation:

7/11x+x=90

We move all terms to the left:

7/11x+x-(90)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We add all the numbers together, and all the variables

x+7/11x-90=0

We multiply all the terms by the denominator


x*11x-90*11x+7=0

Wy multiply elements

11x^2-990x+7=0

a = 11; b = -990; c = +7;
Δ = b2-4ac
Δ = -9902-4·11·7
Δ = 979792
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:

$\sqrt{\Delta}=\sqrt{979792}=\sqrt{16*61237}=\sqrt{16}*\sqrt{61237}=4\sqrt{61237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-990)-4\sqrt{61237}}{2*11}=\frac{990-4\sqrt{61237}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-990)+4\sqrt{61237}}{2*11}=\frac{990+4\sqrt{61237}}{22}
$