48m(m+3)-102=6(8m+7)

Solution for 48m(m+3)-102=6(8m+7) equation:

48m(m+3)-102=6(8m+7)

We move all terms to the left:

48m(m+3)-102-(6(8m+7))=0

We multiply parentheses

48m^2+144m-(6(8m+7))-102=0


We calculate terms in parentheses: -(6(8m+7)), so:

6(8m+7)

We multiply parentheses

48m+42

Back to the equation:

-(48m+42)


We get rid of parentheses

48m^2+144m-48m-42-102=0

We add all the numbers together, and all the variables

48m^2+96m-144=0

a = 48; b = 96; c = -144;
Δ = b2-4ac
Δ = 962-4·48·(-144)
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-192}{2*48}=\frac{-288}{96}
=-3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+192}{2*48}=\frac{96}{96}
=1
$