x^2+3x=9/4

Solution for x^2+3x=9/4 equation:

x^2+3x=9/4

We move all terms to the left:

x^2+3x-(9/4)=0

We add all the numbers together, and all the variables

x^2+3x-(+9/4)=0

We get rid of parentheses

x^2+3x-9/4=0

We multiply all the terms by the denominator


x^2*4+3x*4-9=0

Wy multiply elements

4x^2+12x-9=0

a = 4; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·4·(-9)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*4}=\frac{-12-12\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*4}=\frac{-12+12\sqrt{2}}{8}
$