4y^2-10y-7=0

Solution for 4y^2-10y-7=0 equation:

4y^2-10y-7=0

a = 4; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·4·(-7)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{53}}{2*4}=\frac{10-2\sqrt{53}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{53}}{2*4}=\frac{10+2\sqrt{53}}{8}
$