x(x+5)+7(x+5)=16(x+5)

Solution for x(x+5)+7(x+5)=16(x+5) equation:

x(x+5)+7(x+5)=16(x+5)

We move all terms to the left:

x(x+5)+7(x+5)-(16(x+5))=0

We multiply parentheses

x^2+5x+7x-(16(x+5))+35=0


We calculate terms in parentheses: -(16(x+5)), so:

16(x+5)

We multiply parentheses

16x+80

Back to the equation:

-(16x+80)


We add all the numbers together, and all the variables

x^2+12x-(16x+80)+35=0

We get rid of parentheses

x^2+12x-16x-80+35=0

We add all the numbers together, and all the variables

x^2-4x-45=0

a = 1; b = -4; c = -45;
Δ = b2-4ac
Δ = -42-4·1·(-45)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*1}=\frac{18}{2}
=9
$