2x^2-5x+50+4x^2+6x+60=180

Solution for 2x^2-5x+50+4x^2+6x+60=180 equation:

2x^2-5x+50+4x^2+6x+60=180

We move all terms to the left:

2x^2-5x+50+4x^2+6x+60-(180)=0

We add all the numbers together, and all the variables

6x^2+x-70=0

a = 6; b = 1; c = -70;
Δ = b2-4ac
Δ = 12-4·6·(-70)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-41}{2*6}=\frac{-42}{12}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+41}{2*6}=\frac{40}{12}
=3+1/3
$