-45+17x+6x2=0

Solution for -45+17x+6x2=0 equation:

-45+17x+6x^2=0

a = 6; b = 17; c = -45;
Δ = b2-4ac
Δ = 172-4·6·(-45)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-37}{2*6}=\frac{-54}{12}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+37}{2*6}=\frac{20}{12}
=1+2/3
$