x^2+5x-6=15/4

Solution for x^2+5x-6=15/4 equation:

x^2+5x-6=15/4

We move all terms to the left:

x^2+5x-6-(15/4)=0

We add all the numbers together, and all the variables

x^2+5x-6-(+15/4)=0

We get rid of parentheses

x^2+5x-6-15/4=0

We multiply all the terms by the denominator


x^2*4+5x*4-15-6*4=0

We add all the numbers together, and all the variables

x^2*4+5x*4-39=0

Wy multiply elements

4x^2+20x-39=0

a = 4; b = 20; c = -39;
Δ = b2-4ac
Δ = 202-4·4·(-39)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-32}{2*4}=\frac{-52}{8}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+32}{2*4}=\frac{12}{8}
=1+1/2
$