42x-0.7x^2=30

Solution for 42x-0.7x^2=30 equation:

42x-0.7x^2=30

We move all terms to the left:

42x-0.7x^2-(30)=0

a = -0.7; b = 42; c = -30;
Δ = b2-4ac
Δ = 422-4·(-0.7)·(-30)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-4\sqrt{105}}{2*-0.7}=\frac{-42-4\sqrt{105}}{-1.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+4\sqrt{105}}{2*-0.7}=\frac{-42+4\sqrt{105}}{-1.4}
$