6x^2+30x+23=0

Solution for 6x^2+30x+23=0 equation:

6x^2+30x+23=0

a = 6; b = 30; c = +23;
Δ = b2-4ac
Δ = 302-4·6·23
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{87}}{2*6}=\frac{-30-2\sqrt{87}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{87}}{2*6}=\frac{-30+2\sqrt{87}}{12}
$