2n^2+5n-45=7

Solution for 2n^2+5n-45=7 equation:

2n^2+5n-45=7

We move all terms to the left:

2n^2+5n-45-(7)=0

We add all the numbers together, and all the variables

2n^2+5n-52=0

a = 2; b = 5; c = -52;
Δ = b2-4ac
Δ = 52-4·2·(-52)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-21}{2*2}=\frac{-26}{4}
=-6+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+21}{2*2}=\frac{16}{4}
=4
$