3*20x/2-3x^2/2=85

Solution for 3*20x/2-3x^2/2=85 equation:

3*20x/2-3x^2/2=85

We move all terms to the left:

3*20x/2-3x^2/2-(85)=0

We multiply all the terms by the denominator


-3x^2+3*20x-85*2=0

We add all the numbers together, and all the variables

-3x^2+3*20x-170=0

Wy multiply elements

-3x^2+60x-170=0

a = -3; b = 60; c = -170;
Δ = b2-4ac
Δ = 602-4·(-3)·(-170)
Δ = 1560
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:

$\sqrt{\Delta}=\sqrt{1560}=\sqrt{4*390}=\sqrt{4}*\sqrt{390}=2\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{390}}{2*-3}=\frac{-60-2\sqrt{390}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{390}}{2*-3}=\frac{-60+2\sqrt{390}}{-6}
$