7y^2-43y+4=0

Solution for 7y^2-43y+4=0 equation:

7y^2-43y+4=0

a = 7; b = -43; c = +4;
Δ = b2-4ac
Δ = -432-4·7·4
Δ = 1737
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1737}=\sqrt{9*193}=\sqrt{9}*\sqrt{193}=3\sqrt{193}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-3\sqrt{193}}{2*7}=\frac{43-3\sqrt{193}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+3\sqrt{193}}{2*7}=\frac{43+3\sqrt{193}}{14}
$