49x^2-14x-34=10

Solution for 49x^2-14x-34=10 equation:

49x^2-14x-34=10

We move all terms to the left:

49x^2-14x-34-(10)=0

We add all the numbers together, and all the variables

49x^2-14x-44=0

a = 49; b = -14; c = -44;
Δ = b2-4ac
Δ = -142-4·49·(-44)
Δ = 8820
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:

$\sqrt{\Delta}=\sqrt{8820}=\sqrt{1764*5}=\sqrt{1764}*\sqrt{5}=42\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-42\sqrt{5}}{2*49}=\frac{14-42\sqrt{5}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+42\sqrt{5}}{2*49}=\frac{14+42\sqrt{5}}{98}
$