x2-24x+62=-9x+6

Solution for x2-24x+62=-9x+6 equation:

x2-24x+62=-9x+6

We move all terms to the left:

x2-24x+62-(-9x+6)=0

We add all the numbers together, and all the variables

x^2-24x-(-9x+6)+62=0

We get rid of parentheses

x^2-24x+9x-6+62=0

We add all the numbers together, and all the variables

x^2-15x+56=0

a = 1; b = -15; c = +56;
Δ = b2-4ac
Δ = -152-4·1·56
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-1}{2*1}=\frac{14}{2}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+1}{2*1}=\frac{16}{2}
=8
$