7/2x+5=x+15/3

Solution for 7/2x+5=x+15/3 equation:

7/2x+5=x+15/3

We move all terms to the left:

7/2x+5-(x+15/3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7/2x-x-5+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

-2x^2-10x+10x+7=0

We add all the numbers together, and all the variables

-2x^2+7=0

a = -2; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-2)·7
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*-2}=\frac{0-2\sqrt{14}}{-4}
=-\frac{2\sqrt{14}}{-4}
=-\frac{\sqrt{14}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*-2}=\frac{0+2\sqrt{14}}{-4}
=\frac{2\sqrt{14}}{-4}
=\frac{\sqrt{14}}{-2}
$