X^2-5=-7x+6

Solution for X^2-5=-7x+6 equation:

X^2-5=-7X+6

We move all terms to the left:

X^2-5-(-7X+6)=0

We get rid of parentheses

X^2+7X-6-5=0

We add all the numbers together, and all the variables

X^2+7X-11=0

a = 1; b = 7; c = -11;
Δ = b2-4ac
Δ = 72-4·1·(-11)
Δ = 93
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{93}}{2*1}=\frac{-7-\sqrt{93}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{93}}{2*1}=\frac{-7+\sqrt{93}}{2}
$