7x^2+10x=1

Solution for 7x^2+10x=1 equation:

7x^2+10x=1

We move all terms to the left:

7x^2+10x-(1)=0

a = 7; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·7·(-1)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8\sqrt{2}}{2*7}=\frac{-10-8\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8\sqrt{2}}{2*7}=\frac{-10+8\sqrt{2}}{14}
$