14x^2+83x+65=0

Solution for 14x^2+83x+65=0 equation:

14x^2+83x+65=0

a = 14; b = 83; c = +65;
Δ = b2-4ac
Δ = 832-4·14·65
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(83)-57}{2*14}=\frac{-140}{28}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(83)+57}{2*14}=\frac{-26}{28}
=-13/14
$