6x2+5x=1

Solution for 6x2+5x=1 equation:

6x^2+5x=1

We move all terms to the left:

6x^2+5x-(1)=0

a = 6; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·6·(-1)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*6}=\frac{2}{12}
=1/6
$