x=11/15x+20

Solution for x=11/15x+20 equation:

x=11/15x+20

We move all terms to the left:

x-(11/15x+20)=0


Domain of the equation: 15x+20)!=0

x∈R


We get rid of parentheses

x-11/15x-20=0

We multiply all the terms by the denominator


x*15x-20*15x-11=0

Wy multiply elements

15x^2-300x-11=0

a = 15; b = -300; c = -11;
Δ = b2-4ac
Δ = -3002-4·15·(-11)
Δ = 90660
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:

$\sqrt{\Delta}=\sqrt{90660}=\sqrt{4*22665}=\sqrt{4}*\sqrt{22665}=2\sqrt{22665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-2\sqrt{22665}}{2*15}=\frac{300-2\sqrt{22665}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+2\sqrt{22665}}{2*15}=\frac{300+2\sqrt{22665}}{30}
$