7m2=9(4+m)

Solution for 7m2=9(4+m) equation:

7m^2=9(4+m)

We move all terms to the left:

7m^2-(9(4+m))=0

We add all the numbers together, and all the variables

7m^2-(9(m+4))=0


We calculate terms in parentheses: -(9(m+4)), so:

9(m+4)

We multiply parentheses

9m+36

Back to the equation:

-(9m+36)


We get rid of parentheses

7m^2-9m-36=0

a = 7; b = -9; c = -36;
Δ = b2-4ac
Δ = -92-4·7·(-36)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-33}{2*7}=\frac{-24}{14}
=-1+5/7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+33}{2*7}=\frac{42}{14}
=3
$