X^2+5=3x+10

Solution for X^2+5=3x+10 equation:

X^2+5=3X+10

We move all terms to the left:

X^2+5-(3X+10)=0

We get rid of parentheses

X^2-3X-10+5=0

We add all the numbers together, and all the variables

X^2-3X-5=0

a = 1; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·1·(-5)
Δ = 29
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{29}}{2*1}=\frac{3-\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{29}}{2*1}=\frac{3+\sqrt{29}}{2}
$