14x^2+64x+45=0

Solution for 14x^2+64x+45=0 equation:

14x^2+64x+45=0

a = 14; b = 64; c = +45;
Δ = b2-4ac
Δ = 642-4·14·45
Δ = 1576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1576}=\sqrt{4*394}=\sqrt{4}*\sqrt{394}=2\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-2\sqrt{394}}{2*14}=\frac{-64-2\sqrt{394}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+2\sqrt{394}}{2*14}=\frac{-64+2\sqrt{394}}{28}
$