2a(a-8)+7=5(a+2)-3a-19

Solution for 2a(a-8)+7=5(a+2)-3a-19 equation:

2a(a-8)+7=5(a+2)-3a-19

We move all terms to the left:

2a(a-8)+7-(5(a+2)-3a-19)=0

We multiply parentheses

2a^2-16a-(5(a+2)-3a-19)+7=0


We calculate terms in parentheses: -(5(a+2)-3a-19), so:

5(a+2)-3a-19

We add all the numbers together, and all the variables

-3a+5(a+2)-19

We multiply parentheses

-3a+5a+10-19

We add all the numbers together, and all the variables

2a-9

Back to the equation:

-(2a-9)


We get rid of parentheses

2a^2-16a-2a+9+7=0

We add all the numbers together, and all the variables

2a^2-18a+16=0

a = 2; b = -18; c = +16;
Δ = b2-4ac
Δ = -182-4·2·16
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-14}{2*2}=\frac{4}{4}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+14}{2*2}=\frac{32}{4}
=8
$