x^2+7x/2=22

Solution for x^2+7x/2=22 equation:

x^2+7x/2=22

We move all terms to the left:

x^2+7x/2-(22)=0

We multiply all the terms by the denominator


x^2*2+7x-22*2=0

We add all the numbers together, and all the variables

x^2*2+7x-44=0

Wy multiply elements

2x^2+7x-44=0

a = 2; b = 7; c = -44;
Δ = b2-4ac
Δ = 72-4·2·(-44)
Δ = 401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{401}}{2*2}=\frac{-7-\sqrt{401}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{401}}{2*2}=\frac{-7+\sqrt{401}}{4}
$