10x+55+3x^2=180

Solution for 10x+55+3x^2=180 equation:

10x+55+3x^2=180

We move all terms to the left:

10x+55+3x^2-(180)=0

We add all the numbers together, and all the variables

3x^2+10x-125=0

a = 3; b = 10; c = -125;
Δ = b2-4ac
Δ = 102-4·3·(-125)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-40}{2*3}=\frac{-50}{6}
=-8+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+40}{2*3}=\frac{30}{6}
=5
$