1=7x2+6x

Solution for 1=7x2+6x equation:

1=7x^2+6x

We move all terms to the left:

1-(7x^2+6x)=0

We get rid of parentheses

-7x^2-6x+1=0

a = -7; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-7)·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8}{2*-7}=\frac{-2}{-14}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8}{2*-7}=\frac{14}{-14}
=-1
$