4a(a-9)=5

Solution for 4a(a-9)=5 equation:

4a(a-9)=5

We move all terms to the left:

4a(a-9)-(5)=0

We multiply parentheses

4a^2-36a-5=0

a = 4; b = -36; c = -5;
Δ = b2-4ac
Δ = -362-4·4·(-5)
Δ = 1376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{86}}{2*4}=\frac{36-4\sqrt{86}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{86}}{2*4}=\frac{36+4\sqrt{86}}{8}
$