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5(x+6)-2x=3(x+10)5x+30-2x=3x+303x+30=3x+30-3x-3x^30=30
We move all terms to the left:
5(x+6)-2x-(3(x+10)5x+30-2x)=0
We add all the numbers together, and all the variables
-2x+5(x+6)-(3(x+10)5x+30-2x)=0
We multiply parentheses
-2x+5x-(3(x+10)5x+30-2x)+30=0
We calculate terms in parentheses: -(3(x+10)5x+30-2x), so:We add all the numbers together, and all the variables
3(x+10)5x+30-2x
determiningTheFunctionDomain 3(x+10)5x-2x+30
We add all the numbers together, and all the variables
-2x+3(x+10)5x+30
We multiply parentheses
15x^2-2x+150x+30
We add all the numbers together, and all the variables
15x^2+148x+30
Back to the equation:
-(15x^2+148x+30)
3x-(15x^2+148x+30)+30=0
We get rid of parentheses
-15x^2+3x-148x-30+30=0
We add all the numbers together, and all the variables
-15x^2-145x=0
a = -15; b = -145; c = 0;
Δ = b2-4ac
Δ = -1452-4·(-15)·0
Δ = 21025
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{21025}=145$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-145)-145}{2*-15}=\frac{0}{-30} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-145)+145}{2*-15}=\frac{290}{-30} =-9+2/3 $
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