x2+3x=27/4

Solution for x2+3x=27/4 equation:

x2+3x=27/4

We move all terms to the left:

x2+3x-(27/4)=0

We add all the numbers together, and all the variables

x2+3x-(+27/4)=0

We add all the numbers together, and all the variables

x^2+3x-(+27/4)=0

We get rid of parentheses

x^2+3x-27/4=0

We multiply all the terms by the denominator


x^2*4+3x*4-27=0

Wy multiply elements

4x^2+12x-27=0

a = 4; b = 12; c = -27;
Δ = b2-4ac
Δ = 122-4·4·(-27)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*4}=\frac{-36}{8}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*4}=\frac{12}{8}
=1+1/2
$