7(2m+6)18m=22m+42

Solution for 7(2m+6)18m=22m+42 equation:

7(2m+6)18m=22m+42

We move all terms to the left:

7(2m+6)18m-(22m+42)=0

We multiply parentheses

252m^2+756m-(22m+42)=0

We get rid of parentheses

252m^2+756m-22m-42=0

We add all the numbers together, and all the variables

252m^2+734m-42=0

a = 252; b = 734; c = -42;
Δ = b2-4ac
Δ = 7342-4·252·(-42)
Δ = 581092
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{581092}=\sqrt{4*145273}=\sqrt{4}*\sqrt{145273}=2\sqrt{145273}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(734)-2\sqrt{145273}}{2*252}=\frac{-734-2\sqrt{145273}}{504}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(734)+2\sqrt{145273}}{2*252}=\frac{-734+2\sqrt{145273}}{504}
$