22=m^2+7/4=32

Solution for 22=m^2+7/4=32 equation:

22=m^2+7/4=32

We move all terms to the left:

22-(m^2+7/4)=0

We get rid of parentheses

-m^2+22-7/4=0

We multiply all the terms by the denominator


-m^2*4-7+22*4=0

We add all the numbers together, and all the variables

-m^2*4+81=0

Wy multiply elements

-4m^2+81=0

a = -4; b = 0; c = +81;
Δ = b2-4ac
Δ = 02-4·(-4)·81
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*-4}=\frac{-36}{-8}
=4+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*-4}=\frac{36}{-8}
=-4+1/2
$