2x2-3x=4x+85

Solution for 2x2-3x=4x+85 equation:

2x^2-3x=4x+85

We move all terms to the left:

2x^2-3x-(4x+85)=0

We get rid of parentheses

2x^2-3x-4x-85=0

We add all the numbers together, and all the variables

2x^2-7x-85=0

a = 2; b = -7; c = -85;
Δ = b2-4ac
Δ = -72-4·2·(-85)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-27}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+27}{2*2}=\frac{34}{4}
=8+1/2
$