90=7/11x+x

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

90=7/11x+x

We move all terms to the left:

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


Domain of the equation: 11x+x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-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}
$