8x^2+54x+37=0

Solution for 8x^2+54x+37=0 equation:

8x^2+54x+37=0

a = 8; b = 54; c = +37;
Δ = b2-4ac
Δ = 542-4·8·37
Δ = 1732
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:

$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{433}}{2*8}=\frac{-54-2\sqrt{433}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{433}}{2*8}=\frac{-54+2\sqrt{433}}{16}
$