X2-3x+16=5x+15

Solution for X2-3x+16=5x+15 equation:

X2-3X+16=5X+15

We move all terms to the left:

X2-3X+16-(5X+15)=0

We add all the numbers together, and all the variables

X^2-3X-(5X+15)+16=0

We get rid of parentheses

X^2-3X-5X-15+16=0

We add all the numbers together, and all the variables

X^2-8X+1=0

a = 1; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·1·1
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{15}}{2*1}=\frac{8-2\sqrt{15}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{15}}{2*1}=\frac{8+2\sqrt{15}}{2}
$