7x^2-10x-4=0

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

7x^2-10x-4=0

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

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{53}}{2*7}=\frac{10-2\sqrt{53}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{53}}{2*7}=\frac{10+2\sqrt{53}}{14}
$