<s>[INST] Multiplied X in Quadratic Equation - Delta always lower than 0 I'm new to Quadratic Equations and I am following the two formulas to find $x_1$ and $x_2$ and they are:
$\Delta = b^2 - 4ac$
$x = \dfrac{-(b) \pm \sqrt\Delta}{2a}$
but delta always gives a negative number;
for example I have the following equation:
$6x^2 + 11x - 35 = 0$
What I did was:
1. Calculate the Delta ($\Delta$) by using the formula above
$11^2 - 4ac$
$11^2 = 121$ and  $4ac = -840 = 4\times6\times(-35)$
$\Delta = 121 - 840 = 719$
and got $-719$ as result
 [/INST] $6x^2+11x−35=0$
$a =6; b= 11; c= -35$
$b^2 = 121$.
$4ac = 4*6*(-35) =-840$
$b^2 - 4ac = 121 - (-840) = 121 + 841 = 961=31$.
So $\Delta = 961=31^2 > 0$ and $\sqrt{961} = 31$
$x = \frac {-11 \pm 31}{2*6}$.
$x = \frac {-42}{12}$ or $x = \frac {20}{12}$
$x = -\frac 72$ or $x = \frac 53$
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