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7=5x+3x(x-2)+5
We move all terms to the left:
7-(5x+3x(x-2)+5)=0
We calculate terms in parentheses: -(5x+3x(x-2)+5), so:We get rid of parentheses
5x+3x(x-2)+5
We multiply parentheses
3x^2+5x-6x+5
We add all the numbers together, and all the variables
3x^2-1x+5
Back to the equation:
-(3x^2-1x+5)
-3x^2+1x-5+7=0
We add all the numbers together, and all the variables
-3x^2+x+2=0
a = -3; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-3)·2
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-3}=\frac{-6}{-6} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-3}=\frac{4}{-6} =-2/3 $
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