m^2+19m+90=7

Solution for m^2+19m+90=7 equation:

m^2+19m+90=7

We move all terms to the left:

m^2+19m+90-(7)=0

We add all the numbers together, and all the variables

m^2+19m+83=0

a = 1; b = 19; c = +83;
Δ = b2-4ac
Δ = 192-4·1·83
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{29}}{2*1}=\frac{-19-\sqrt{29}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{29}}{2*1}=\frac{-19+\sqrt{29}}{2}
$