4k^2-23k+4=0

Solution for 4k^2-23k+4=0 equation:

4k^2-23k+4=0

a = 4; b = -23; c = +4;
Δ = b2-4ac
Δ = -232-4·4·4
Δ = 465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{465}}{2*4}=\frac{23-\sqrt{465}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{465}}{2*4}=\frac{23+\sqrt{465}}{8}
$