M=5/4n-7n=40

Solution for M=5/4n-7n=40 equation:

=5/4M-7M=40

We move all terms to the left:

-(5/4M-7M)=0


Domain of the equation: 4M-7M)!=0

M∈R


We add all the numbers together, and all the variables

-(-7M+5/4M)=0

We get rid of parentheses

7M-5/4M=0

We multiply all the terms by the denominator


7M*4M-5=0

Wy multiply elements

28M^2-5=0

a = 28; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·28·(-5)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{35}}{2*28}=\frac{0-4\sqrt{35}}{56}
=-\frac{4\sqrt{35}}{56}
=-\frac{\sqrt{35}}{14}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{35}}{2*28}=\frac{0+4\sqrt{35}}{56}
=\frac{4\sqrt{35}}{56}
=\frac{\sqrt{35}}{14}
$