7x-22/2x+8=3

Solution for 7x-22/2x+8=3 equation:

7x-22/2x+8=3

We move all terms to the left:

7x-22/2x+8-(3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7x-22/2x+5=0

We multiply all the terms by the denominator


7x*2x+5*2x-22=0

Wy multiply elements

14x^2+10x-22=0

a = 14; b = 10; c = -22;
Δ = b2-4ac
Δ = 102-4·14·(-22)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{37}}{2*14}=\frac{-10-6\sqrt{37}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{37}}{2*14}=\frac{-10+6\sqrt{37}}{28}
$