90=m(m+46)

Solution for 90=m(m+46) equation:

90=m(m+46)

We move all terms to the left:

90-(m(m+46))=0


We calculate terms in parentheses: -(m(m+46)), so:

m(m+46)

We multiply parentheses

m^2+46m

Back to the equation:

-(m^2+46m)


We get rid of parentheses

-m^2-46m+90=0

We add all the numbers together, and all the variables

-1m^2-46m+90=0

a = -1; b = -46; c = +90;
Δ = b2-4ac
Δ = -462-4·(-1)·90
Δ = 2476
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:

$\sqrt{\Delta}=\sqrt{2476}=\sqrt{4*619}=\sqrt{4}*\sqrt{619}=2\sqrt{619}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{619}}{2*-1}=\frac{46-2\sqrt{619}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{619}}{2*-1}=\frac{46+2\sqrt{619}}{-2}
$