5m^2=7m+90

Solution for 5m^2=7m+90 equation:

5m^2=7m+90

We move all terms to the left:

5m^2-(7m+90)=0

We get rid of parentheses

5m^2-7m-90=0

a = 5; b = -7; c = -90;
Δ = b2-4ac
Δ = -72-4·5·(-90)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-43}{2*5}=\frac{-36}{10}
=-3+3/5
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+43}{2*5}=\frac{50}{10}
=5
$