4x^2+48x=81

Solution for 4x^2+48x=81 equation:

4x^2+48x=81

We move all terms to the left:

4x^2+48x-(81)=0

a = 4; b = 48; c = -81;
Δ = b2-4ac
Δ = 482-4·4·(-81)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-60}{2*4}=\frac{-108}{8}
=-13+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+60}{2*4}=\frac{12}{8}
=1+1/2
$