X^2+5y=10

Solution for X^2+5y=10 equation:

X^2+5X=10

We move all terms to the left:

X^2+5X-(10)=0

a = 1; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·1·(-10)
Δ = 65
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{-(5)-\sqrt{65}}{2*1}=\frac{-5-\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*1}=\frac{-5+\sqrt{65}}{2}
$