7x+50=17/2x+11

Solution for 7x+50=17/2x+11 equation:

7x+50=17/2x+11

We move all terms to the left:

7x+50-(17/2x+11)=0


Domain of the equation: 2x+11)!=0

x∈R


We get rid of parentheses

7x-17/2x-11+50=0

We multiply all the terms by the denominator


7x*2x-11*2x+50*2x-17=0

Wy multiply elements

14x^2-22x+100x-17=0

We add all the numbers together, and all the variables

14x^2+78x-17=0

a = 14; b = 78; c = -17;
Δ = b2-4ac
Δ = 782-4·14·(-17)
Δ = 7036
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:

$\sqrt{\Delta}=\sqrt{7036}=\sqrt{4*1759}=\sqrt{4}*\sqrt{1759}=2\sqrt{1759}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1759}}{2*14}=\frac{-78-2\sqrt{1759}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1759}}{2*14}=\frac{-78+2\sqrt{1759}}{28}
$