X2+x=7x+16

Solution for X2+x=7x+16 equation:

X2+X=7X+16

We move all terms to the left:

X2+X-(7X+16)=0

We add all the numbers together, and all the variables

X^2+X-(7X+16)=0

We get rid of parentheses

X^2+X-7X-16=0

We add all the numbers together, and all the variables

X^2-6X-16=0

a = 1; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·1·(-16)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*1}=\frac{16}{2}
=8
$