x^2+5x=23/4

Solution for x^2+5x=23/4 equation:

x^2+5x=23/4

We move all terms to the left:

x^2+5x-(23/4)=0

We add all the numbers together, and all the variables

x^2+5x-(+23/4)=0

We get rid of parentheses

x^2+5x-23/4=0

We multiply all the terms by the denominator


x^2*4+5x*4-23=0

Wy multiply elements

4x^2+20x-23=0

a = 4; b = 20; c = -23;
Δ = b2-4ac
Δ = 202-4·4·(-23)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-16\sqrt{3}}{2*4}=\frac{-20-16\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+16\sqrt{3}}{2*4}=\frac{-20+16\sqrt{3}}{8}
$