4n(2n+5)=3n+10

Solution for 4n(2n+5)=3n+10 equation:

4n(2n+5)=3n+10

We move all terms to the left:

4n(2n+5)-(3n+10)=0

We multiply parentheses

8n^2+20n-(3n+10)=0

We get rid of parentheses

8n^2+20n-3n-10=0

We add all the numbers together, and all the variables

8n^2+17n-10=0

a = 8; b = 17; c = -10;
Δ = b2-4ac
Δ = 172-4·8·(-10)
Δ = 609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{609}}{2*8}=\frac{-17-\sqrt{609}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{609}}{2*8}=\frac{-17+\sqrt{609}}{16}
$