3x^2-10x-23=-4

Solution for 3x^2-10x-23=-4 equation:

3x^2-10x-23=-4

We move all terms to the left:

3x^2-10x-23-(-4)=0

We add all the numbers together, and all the variables

3x^2-10x-19=0

a = 3; b = -10; c = -19;
Δ = b2-4ac
Δ = -102-4·3·(-19)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{82}}{2*3}=\frac{10-2\sqrt{82}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{82}}{2*3}=\frac{10+2\sqrt{82}}{6}
$