2x^2+11x^2+12x=20

Solution for 2x^2+11x^2+12x=20 equation:

2x^2+11x^2+12x=20

We move all terms to the left:

2x^2+11x^2+12x-(20)=0

We add all the numbers together, and all the variables

13x^2+12x-20=0

a = 13; b = 12; c = -20;
Δ = b2-4ac
Δ = 122-4·13·(-20)
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{74}}{2*13}=\frac{-12-4\sqrt{74}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{74}}{2*13}=\frac{-12+4\sqrt{74}}{26}
$