4x^2+120-2X^2+19x=180

Solution for 4x^2+120-2X^2+19x=180 equation:

4x^2+120-2x^2+19x=180

We move all terms to the left:

4x^2+120-2x^2+19x-(180)=0

We add all the numbers together, and all the variables

2x^2+19x-60=0

a = 2; b = 19; c = -60;
Δ = b2-4ac
Δ = 192-4·2·(-60)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-29}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+29}{2*2}=\frac{10}{4}
=2+1/2
$