4x+27+2x^2-11x=180

Solution for 4x+27+2x^2-11x=180 equation:

4x+27+2x^2-11x=180

We move all terms to the left:

4x+27+2x^2-11x-(180)=0

We add all the numbers together, and all the variables

2x^2-7x-153=0

a = 2; b = -7; c = -153;
Δ = b2-4ac
Δ = -72-4·2·(-153)
Δ = 1273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{1273}}{2*2}=\frac{7-\sqrt{1273}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1273}}{2*2}=\frac{7+\sqrt{1273}}{4}
$