2x^2+3x^2-44x+60=0

Solution for 2x^2+3x^2-44x+60=0 equation:

2x^2+3x^2-44x+60=0

We add all the numbers together, and all the variables

5x^2-44x+60=0

a = 5; b = -44; c = +60;
Δ = b2-4ac
Δ = -442-4·5·60
Δ = 736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{46}}{2*5}=\frac{44-4\sqrt{46}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{46}}{2*5}=\frac{44+4\sqrt{46}}{10}
$