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

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Solution for 2x^2-3x=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 $

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