4x2=27x+81

Solution for 4x2=27x+81 equation:

4x^2=27x+81

We move all terms to the left:

4x^2-(27x+81)=0

We get rid of parentheses

4x^2-27x-81=0

a = 4; b = -27; c = -81;
Δ = b2-4ac
Δ = -272-4·4·(-81)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-45}{2*4}=\frac{-18}{8}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+45}{2*4}=\frac{72}{8}
=9
$