85=(3x+2)X

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Solution for 85=(3x+2)X equation:



85=(3x+2)x
We move all terms to the left:
85-((3x+2)x)=0
We calculate terms in parentheses: -((3x+2)x), so:
(3x+2)x
We multiply parentheses
3x^2+2x
Back to the equation:
-(3x^2+2x)
We get rid of parentheses
-3x^2-2x+85=0
a = -3; b = -2; c = +85;
Δ = b2-4ac
Δ = -22-4·(-3)·85
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-32}{2*-3}=\frac{-30}{-6} =+5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+32}{2*-3}=\frac{34}{-6} =-5+2/3 $

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