5a^2-45a=-101

Solution for 5a^2-45a=-101 equation:

5a^2-45a=-101

We move all terms to the left:

5a^2-45a-(-101)=0

We add all the numbers together, and all the variables

5a^2-45a+101=0

a = 5; b = -45; c = +101;
Δ = b2-4ac
Δ = -452-4·5·101
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{5}}{2*5}=\frac{45-\sqrt{5}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{5}}{2*5}=\frac{45+\sqrt{5}}{10}
$