X^2-7x+3=12

Solution for X^2-7x+3=12 equation:

X^2-7X+3=12

We move all terms to the left:

X^2-7X+3-(12)=0

We add all the numbers together, and all the variables

X^2-7X-9=0

a = 1; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·1·(-9)
Δ = 85
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{85}}{2*1}=\frac{7-\sqrt{85}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{85}}{2*1}=\frac{7+\sqrt{85}}{2}
$