m=4/5m-7

Solution for m=4/5m-7 equation:

m=4/5m-7

We move all terms to the left:

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


Domain of the equation: 5m-7)!=0

m∈R


We get rid of parentheses

m-4/5m+7=0

We multiply all the terms by the denominator


m*5m+7*5m-4=0

Wy multiply elements

5m^2+35m-4=0

a = 5; b = 35; c = -4;
Δ = b2-4ac
Δ = 352-4·5·(-4)
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-3\sqrt{145}}{2*5}=\frac{-35-3\sqrt{145}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+3\sqrt{145}}{2*5}=\frac{-35+3\sqrt{145}}{10}
$