x^2+7x+25/4=97/4

Solution for x^2+7x+25/4=97/4 equation:

x^2+7x+25/4=97/4

We move all terms to the left:

x^2+7x+25/4-(97/4)=0

We add all the numbers together, and all the variables

x^2+7x+25/4-(+97/4)=0

We get rid of parentheses

x^2+7x+25/4-97/4=0

We multiply all the terms by the denominator


x^2*4+7x*4+25-97=0

We add all the numbers together, and all the variables

x^2*4+7x*4-72=0

Wy multiply elements

4x^2+28x-72=0

a = 4; b = 28; c = -72;
Δ = b2-4ac
Δ = 282-4·4·(-72)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-44}{2*4}=\frac{-72}{8}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+44}{2*4}=\frac{16}{8}
=2
$