x^2+3x=25/4

Solution for x^2+3x=25/4 equation:

x^2+3x=25/4

We move all terms to the left:

x^2+3x-(25/4)=0

We add all the numbers together, and all the variables

x^2+3x-(+25/4)=0

We get rid of parentheses

x^2+3x-25/4=0

We multiply all the terms by the denominator


x^2*4+3x*4-25=0

Wy multiply elements

4x^2+12x-25=0

a = 4; b = 12; c = -25;
Δ = b2-4ac
Δ = 122-4·4·(-25)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{34}}{2*4}=\frac{-12-4\sqrt{34}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{34}}{2*4}=\frac{-12+4\sqrt{34}}{8}
$