5j+7=2(2j+1)5j+7=2(2j+1)

Solution for 5j+7=2(2j+1)5j+7=2(2j+1) equation:

5j+7=2(2j+1)5j+7=2(2j+1)

We move all terms to the left:

5j+7-(2(2j+1)5j+7)=0


We calculate terms in parentheses: -(2(2j+1)5j+7), so:

2(2j+1)5j+7

We multiply parentheses

20j^2+10j+7

Back to the equation:

-(20j^2+10j+7)


We get rid of parentheses

-20j^2+5j-10j-7+7=0

We add all the numbers together, and all the variables

-20j^2-5j=0

a = -20; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-20)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-20}=\frac{0}{-40}
=0
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-20}=\frac{10}{-40}
=-1/4
$