x=9/10x+6=11

Solution for x=9/10x+6=11 equation:

x=9/10x+6=11

We move all terms to the left:

x-(9/10x+6)=0


Domain of the equation: 10x+6)!=0

x∈R


We get rid of parentheses

x-9/10x-6=0

We multiply all the terms by the denominator


x*10x-6*10x-9=0

Wy multiply elements

10x^2-60x-9=0

a = 10; b = -60; c = -9;
Δ = b2-4ac
Δ = -602-4·10·(-9)
Δ = 3960
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:

$\sqrt{\Delta}=\sqrt{3960}=\sqrt{36*110}=\sqrt{36}*\sqrt{110}=6\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{110}}{2*10}=\frac{60-6\sqrt{110}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{110}}{2*10}=\frac{60+6\sqrt{110}}{20}
$