2/2+x=9/5x+7

Solution for 2/2+x=9/5x+7 equation:

2/2+x=9/5x+7

We move all terms to the left:

2/2+x-(9/5x+7)=0


Domain of the equation: 5x+7)!=0

x∈R


We add all the numbers together, and all the variables

x-(9/5x+7)+1=0

We get rid of parentheses

x-9/5x-7+1=0

We multiply all the terms by the denominator


x*5x-7*5x+1*5x-9=0

Wy multiply elements

5x^2-35x+5x-9=0

We add all the numbers together, and all the variables

5x^2-30x-9=0

a = 5; b = -30; c = -9;
Δ = b2-4ac
Δ = -302-4·5·(-9)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{30}}{2*5}=\frac{30-6\sqrt{30}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{30}}{2*5}=\frac{30+6\sqrt{30}}{10}
$