4x2+16x+27=180

Solution for 4x2+16x+27=180 equation:

4x^2+16x+27=180

We move all terms to the left:

4x^2+16x+27-(180)=0

We add all the numbers together, and all the variables

4x^2+16x-153=0

a = 4; b = 16; c = -153;
Δ = b2-4ac
Δ = 162-4·4·(-153)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-52}{2*4}=\frac{-68}{8}
=-8+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+52}{2*4}=\frac{36}{8}
=4+1/2
$