7x^2-10x-7=0

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

7x^2-10x-7=0

a = 7; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·7·(-7)
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{74}}{2*7}=\frac{10-2\sqrt{74}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{74}}{2*7}=\frac{10+2\sqrt{74}}{14}
$