5(e+6)=4(e+7)e

Solution for 5(e+6)=4(e+7)e equation:

5(e+6)=4(e+7)e

We move all terms to the left:

5(e+6)-(4(e+7)e)=0

We multiply parentheses

5e-(4(e+7)e)+30=0


We calculate terms in parentheses: -(4(e+7)e), so:

4(e+7)e

We multiply parentheses

4e^2+28e

Back to the equation:

-(4e^2+28e)


We get rid of parentheses

-4e^2+5e-28e+30=0

We add all the numbers together, and all the variables

-4e^2-23e+30=0

a = -4; b = -23; c = +30;
Δ = b2-4ac
Δ = -232-4·(-4)·30
Δ = 1009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{1009}}{2*-4}=\frac{23-\sqrt{1009}}{-8}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1009}}{2*-4}=\frac{23+\sqrt{1009}}{-8}
$