x^2=7x+6=6

Solution for x^2=7x+6=6 equation:

x^2=7x+6=6

We move all terms to the left:

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

We get rid of parentheses

x^2-7x-6=0

a = 1; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·1·(-6)
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*1}=\frac{7-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{73}}{2*1}=\frac{7+\sqrt{73}}{2}
$