13x-21x^2+23=0

Solution for 13x-21x^2+23=0 equation:

13x-21x^2+23=0

a = -21; b = 13; c = +23;
Δ = b2-4ac
Δ = 132-4·(-21)·23
Δ = 2101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{2101}}{2*-21}=\frac{-13-\sqrt{2101}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{2101}}{2*-21}=\frac{-13+\sqrt{2101}}{-42}
$