14x^2+70x-336=1

Solution for 14x^2+70x-336=1 equation:

14x^2+70x-336=1

We move all terms to the left:

14x^2+70x-336-(1)=0

We add all the numbers together, and all the variables

14x^2+70x-337=0

a = 14; b = 70; c = -337;
Δ = b2-4ac
Δ = 702-4·14·(-337)
Δ = 23772
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:

$\sqrt{\Delta}=\sqrt{23772}=\sqrt{4*5943}=\sqrt{4}*\sqrt{5943}=2\sqrt{5943}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{5943}}{2*14}=\frac{-70-2\sqrt{5943}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{5943}}{2*14}=\frac{-70+2\sqrt{5943}}{28}
$