5x-13=5/2x+7

Solution for 5x-13=5/2x+7 equation:

5x-13=5/2x+7

We move all terms to the left:

5x-13-(5/2x+7)=0


Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

5x-5/2x-7-13=0

We multiply all the terms by the denominator


5x*2x-7*2x-13*2x-5=0

Wy multiply elements

10x^2-14x-26x-5=0

We add all the numbers together, and all the variables

10x^2-40x-5=0

a = 10; b = -40; c = -5;
Δ = b2-4ac
Δ = -402-4·10·(-5)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-30\sqrt{2}}{2*10}=\frac{40-30\sqrt{2}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+30\sqrt{2}}{2*10}=\frac{40+30\sqrt{2}}{20}
$