1/2(3m)(m)=6.75m^2

Solution for 1/2(3m)(m)=6.75m^2 equation:

1/2(3m)(m)=6.75m^2

We move all terms to the left:

1/2(3m)(m)-(6.75m^2)=0


Domain of the equation: 23mm!=0

m!=0/1

m!=0

m∈R


We get rid of parentheses

-6.75m^2+1/23mm=0

We multiply all the terms by the denominator


-(6.75m^2)*23mm+1=0

We multiply parentheses

-138m^2+1=0

a = -138; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-138)·1
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{138}}{2*-138}=\frac{0-2\sqrt{138}}{-276}
=-\frac{2\sqrt{138}}{-276}
=-\frac{\sqrt{138}}{-138}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{138}}{2*-138}=\frac{0+2\sqrt{138}}{-276}
=\frac{2\sqrt{138}}{-276}
=\frac{\sqrt{138}}{-138}
$