12x+5x^2=65

Solution for 12x+5x^2=65 equation:

12x+5x^2=65

We move all terms to the left:

12x+5x^2-(65)=0

a = 5; b = 12; c = -65;
Δ = b2-4ac
Δ = 122-4·5·(-65)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-38}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+38}{2*5}=\frac{26}{10}
=2+3/5
$