m2+10=15m-34

Solution for m2+10=15m-34 equation:

m2+10=15m-34

We move all terms to the left:

m2+10-(15m-34)=0

We add all the numbers together, and all the variables

m^2-(15m-34)+10=0

We get rid of parentheses

m^2-15m+34+10=0

We add all the numbers together, and all the variables

m^2-15m+44=0

a = 1; b = -15; c = +44;
Δ = b2-4ac
Δ = -152-4·1·44
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{-(-15)-7}{2*1}=\frac{8}{2}
=4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+7}{2*1}=\frac{22}{2}
=11
$