6x2=7x+1

Solution for 6x2=7x+1 equation:

6x^2=7x+1

We move all terms to the left:

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

We get rid of parentheses

6x^2-7x-1=0

a = 6; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·6·(-1)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{73}}{2*6}=\frac{7-\sqrt{73}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{73}}{2*6}=\frac{7+\sqrt{73}}{12}
$