/6x+11=3x-10

Solution for /6x+11=3x-10 equation:

/6x+11=3x-10

We move all terms to the left:

/6x+11-(3x-10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

/6x-3x+10+11=0

We multiply all the terms by the denominator


-3x*6x+10*6x+11*6x+=0

We add all the numbers together, and all the variables

-3x*6x+10*6x+11*6x=0

Wy multiply elements

-18x^2+60x+66x=0

We add all the numbers together, and all the variables

-18x^2+126x=0

a = -18; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·(-18)·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*-18}=\frac{-252}{-36}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*-18}=\frac{0}{-36}
=0
$