(2a+1)(a-7)=0

Solution for (2a+1)(a-7)=0 equation:

(2a+1)(a-7)=0

We multiply parentheses ..

(+2a^2-14a+a-7)=0

We get rid of parentheses

2a^2-14a+a-7=0

We add all the numbers together, and all the variables

2a^2-13a-7=0

a = 2; b = -13; c = -7;
Δ = b2-4ac
Δ = -132-4·2·(-7)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-15}{2*2}=\frac{-2}{4}
=-1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+15}{2*2}=\frac{28}{4}
=7
$