42.7x-0.7x^2=588

Solution for 42.7x-0.7x^2=588 equation:

42.7x-0.7x^2=588

We move all terms to the left:

42.7x-0.7x^2-(588)=0

a = -0.7; b = 42.7; c = -588;
Δ = b2-4ac
Δ = 42.72-4·(-0.7)·(-588)
Δ = 176.89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42.7)-\sqrt{176.89}}{2*-0.7}=\frac{-42.7-\sqrt{176.89}}{-1.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42.7)+\sqrt{176.89}}{2*-0.7}=\frac{-42.7+\sqrt{176.89}}{-1.4}
$