x^2+x=7x+16x2+x=7x+16

Solution for x^2+x=7x+16x2+x=7x+16 equation:

x^2+x=7x+16x^2+x=7x+16

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-15x^2-7x=0

a = -15; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-15)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-15}=\frac{14}{-30}
=-7/15
$