X^2+51=-15x+1

Solution for X^2+51=-15x+1 equation:

X^2+51=-15X+1

We move all terms to the left:

X^2+51-(-15X+1)=0

We get rid of parentheses

X^2+15X-1+51=0

We add all the numbers together, and all the variables

X^2+15X+50=0

a = 1; b = 15; c = +50;
Δ = b2-4ac
Δ = 152-4·1·50
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5}{2*1}=\frac{-20}{2}
=-10
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5}{2*1}=\frac{-10}{2}
=-5
$