4x+5x2=180

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Solution for 4x+5x2=180 equation:



4x+5x^2=180
We move all terms to the left:
4x+5x^2-(180)=0
a = 5; b = 4; c = -180;
Δ = b2-4ac
Δ = 42-4·5·(-180)
Δ = 3616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{226}}{2*5}=\frac{-4-4\sqrt{226}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{226}}{2*5}=\frac{-4+4\sqrt{226}}{10} $

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