x^2-15x+21=7

Solution for x^2-15x+21=7 equation:

x^2-15x+21=7

We move all terms to the left:

x^2-15x+21-(7)=0

We add all the numbers together, and all the variables

x^2-15x+14=0

a = 1; b = -15; c = +14;
Δ = b2-4ac
Δ = -152-4·1·14
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-13}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+13}{2*1}=\frac{28}{2}
=14
$