6x^2+91x+253=0

Solution for 6x^2+91x+253=0 equation:

6x^2+91x+253=0

a = 6; b = 91; c = +253;
Δ = b2-4ac
Δ = 912-4·6·253
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-47}{2*6}=\frac{-138}{12}
=-11+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+47}{2*6}=\frac{-44}{12}
=-3+2/3
$