X^2-25=3x+17

Solution for X^2-25=3x+17 equation:

X^2-25=3X+17

We move all terms to the left:

X^2-25-(3X+17)=0

We get rid of parentheses

X^2-3X-17-25=0

We add all the numbers together, and all the variables

X^2-3X-42=0

a = 1; b = -3; c = -42;
Δ = b2-4ac
Δ = -32-4·1·(-42)
Δ = 177
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{-(-3)-\sqrt{177}}{2*1}=\frac{3-\sqrt{177}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{177}}{2*1}=\frac{3+\sqrt{177}}{2}
$