4*m=3*(m-5)+7*m/2

Solution for 4*m=3*(m-5)+7*m/2 equation:

4m=3(m-5)+7m/2

We move all terms to the left:

4m-(3(m-5)+7m/2)=0

We multiply all the terms by the denominator


4m*2)-(3(m-5)+7m=0

We add all the numbers together, and all the variables

7m+4m*2)-(3(m-5)=0

Wy multiply elements

8m^2+7m=0

a = 8; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·8·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*8}=\frac{-14}{16}
=-7/8
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*8}=\frac{0}{16}
=0
$