11/2x+26=5x-10

Solution for 11/2x+26=5x-10 equation:

11/2x+26=5x-10

We move all terms to the left:

11/2x+26-(5x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

11/2x-5x+10+26=0

We multiply all the terms by the denominator


-5x*2x+10*2x+26*2x+11=0

Wy multiply elements

-10x^2+20x+52x+11=0

We add all the numbers together, and all the variables

-10x^2+72x+11=0

a = -10; b = 72; c = +11;
Δ = b2-4ac
Δ = 722-4·(-10)·11
Δ = 5624
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:

$\sqrt{\Delta}=\sqrt{5624}=\sqrt{4*1406}=\sqrt{4}*\sqrt{1406}=2\sqrt{1406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1406}}{2*-10}=\frac{-72-2\sqrt{1406}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1406}}{2*-10}=\frac{-72+2\sqrt{1406}}{-20}
$