15x^2+38x+14=0

Solution for 15x^2+38x+14=0 equation:

15x^2+38x+14=0

a = 15; b = 38; c = +14;
Δ = b2-4ac
Δ = 382-4·15·14
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{151}}{2*15}=\frac{-38-2\sqrt{151}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{151}}{2*15}=\frac{-38+2\sqrt{151}}{30}
$