X^2+3x-5=4x+16

Solution for X^2+3x-5=4x+16 equation:

X^2+3X-5=4X+16

We move all terms to the left:

X^2+3X-5-(4X+16)=0

We get rid of parentheses

X^2+3X-4X-16-5=0

We add all the numbers together, and all the variables

X^2-1X-21=0

a = 1; b = -1; c = -21;
Δ = b2-4ac
Δ = -12-4·1·(-21)
Δ = 85
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{-(-1)-\sqrt{85}}{2*1}=\frac{1-\sqrt{85}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{85}}{2*1}=\frac{1+\sqrt{85}}{2}
$