178x-4x^2=420

Solution for 178x-4x^2=420 equation:

178x-4x^2=420

We move all terms to the left:

178x-4x^2-(420)=0

a = -4; b = 178; c = -420;
Δ = b2-4ac
Δ = 1782-4·(-4)·(-420)
Δ = 24964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24964}=158$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(178)-158}{2*-4}=\frac{-336}{-8}
=+42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(178)+158}{2*-4}=\frac{-20}{-8}
=2+1/2
$