5/2*x-7=23

Solution for 5/2*x-7=23 equation:

5/2*x-7=23

We move all terms to the left:

5/2*x-7-(23)=0


Domain of the equation: 2*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2*x-30=0

We multiply all the terms by the denominator


-30*2*x+5=0

Wy multiply elements

-60x*x+5=0

Wy multiply elements

-60x^2+5=0

a = -60; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-60)·5
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*-60}=\frac{0-20\sqrt{3}}{-120}
=-\frac{20\sqrt{3}}{-120}
=-\frac{\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*-60}=\frac{0+20\sqrt{3}}{-120}
=\frac{20\sqrt{3}}{-120}
=\frac{\sqrt{3}}{-6}
$