7/11x+10=19-2x

Solution for 7/11x+10=19-2x equation:

7/11x+10=19-2x

We move all terms to the left:

7/11x+10-(19-2x)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We add all the numbers together, and all the variables

7/11x-(-2x+19)+10=0

We get rid of parentheses

7/11x+2x-19+10=0

We multiply all the terms by the denominator


2x*11x-19*11x+10*11x+7=0

Wy multiply elements

22x^2-209x+110x+7=0

We add all the numbers together, and all the variables

22x^2-99x+7=0

a = 22; b = -99; c = +7;
Δ = b2-4ac
Δ = -992-4·22·7
Δ = 9185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-\sqrt{9185}}{2*22}=\frac{99-\sqrt{9185}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{9185}}{2*22}=\frac{99+\sqrt{9185}}{44}
$