(e+4)(e-7)=-30

Solution for (e+4)(e-7)=-30 equation:

(e+4)(e-7)=-30

We move all terms to the left:

(e+4)(e-7)-(-30)=0

We add all the numbers together, and all the variables

(e+4)(e-7)+30=0

We multiply parentheses ..

(+e^2-7e+4e-28)+30=0

We get rid of parentheses

e^2-7e+4e-28+30=0

We add all the numbers together, and all the variables

e^2-3e+2=0

a = 1; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·1·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-1}{2*1}=\frac{2}{2}
=1
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+1}{2*1}=\frac{4}{2}
=2
$