0.6x(2-9x)+1.1(5x-2)=0.5(3x-8)+0.2(15-7x)

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Solution for 0.6x(2-9x)+1.1(5x-2)=0.5(3x-8)+0.2(15-7x) equation:



0.6x(2-9x)+1.1(5x-2)=0.5(3x-8)+0.2(15-7x)
We move all terms to the left:
0.6x(2-9x)+1.1(5x-2)-(0.5(3x-8)+0.2(15-7x))=0
We add all the numbers together, and all the variables
0.6x(-9x+2)+1.1(5x-2)-(0.5(3x-8)+0.2(-7x+15))=0
We multiply parentheses
0x^2+0x+5.5x-(0.5(3x-8)+0.2(-7x+15))-2.2=0
We calculate terms in parentheses: -(0.5(3x-8)+0.2(-7x+15)), so:
0.5(3x-8)+0.2(-7x+15)
We multiply parentheses
1.5x-1.4x-4+3
We add all the numbers together, and all the variables
0.1x-1
Back to the equation:
-(0.1x-1)
We add all the numbers together, and all the variables
x^2+6.5x-(0.1x-1)-2.2=0
We get rid of parentheses
x^2+6.5x-0.1x+1-2.2=0
We add all the numbers together, and all the variables
x^2+6.4x-1.2=0
a = 1; b = 6.4; c = -1.2;
Δ = b2-4ac
Δ = 6.42-4·1·(-1.2)
Δ = 45.76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6.4)-\sqrt{45.76}}{2*1}=\frac{-6.4-\sqrt{45.76}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.4)+\sqrt{45.76}}{2*1}=\frac{-6.4+\sqrt{45.76}}{2} $

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