23x^2+144x-186=0

Solution for 23x^2+144x-186=0 equation:

23x^2+144x-186=0

a = 23; b = 144; c = -186;
Δ = b2-4ac
Δ = 1442-4·23·(-186)
Δ = 37848
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:

$\sqrt{\Delta}=\sqrt{37848}=\sqrt{4*9462}=\sqrt{4}*\sqrt{9462}=2\sqrt{9462}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-2\sqrt{9462}}{2*23}=\frac{-144-2\sqrt{9462}}{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+2\sqrt{9462}}{2*23}=\frac{-144+2\sqrt{9462}}{46}
$