x(5/2-7)=23

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

x(5/2-7)=23

We move all terms to the left:

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

We multiply parentheses

5x^2-7x-23=0

a = 5; b = -7; c = -23;
Δ = b2-4ac
Δ = -72-4·5·(-23)
Δ = 509
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{509}}{2*5}=\frac{7-\sqrt{509}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{509}}{2*5}=\frac{7+\sqrt{509}}{10}
$