(15/4)m=15/2

Solution for (15/4)m=15/2 equation:

(15/4)m=15/2

We move all terms to the left:

(15/4)m-(15/2)=0


Domain of the equation: 4)m!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

(+15/4)m-(+15/2)=0

We multiply parentheses

15m^2-(+15/2)=0

We get rid of parentheses

15m^2-15/2=0

We multiply all the terms by the denominator


15m^2*2-15=0

Wy multiply elements

30m^2-15=0

a = 30; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·30·(-15)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*30}=\frac{0-30\sqrt{2}}{60}
=-\frac{30\sqrt{2}}{60}
=-\frac{\sqrt{2}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*30}=\frac{0+30\sqrt{2}}{60}
=\frac{30\sqrt{2}}{60}
=\frac{\sqrt{2}}{2}
$