4n^2+10n-43=7

Solution for 4n^2+10n-43=7 equation:

4n^2+10n-43=7

We move all terms to the left:

4n^2+10n-43-(7)=0

We add all the numbers together, and all the variables

4n^2+10n-50=0

a = 4; b = 10; c = -50;
Δ = b2-4ac
Δ = 102-4·4·(-50)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*4}=\frac{-40}{8}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*4}=\frac{20}{8}
=2+1/2
$