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5x(-x-11)=5x-7x(-x-7)
We move all terms to the left:
5x(-x-11)-(5x-7x(-x-7))=0
We add all the numbers together, and all the variables
5x(-1x-11)-(5x-7x(-1x-7))=0
We multiply parentheses
-5x^2-55x-(5x-7x(-1x-7))=0
We calculate terms in parentheses: -(5x-7x(-1x-7)), so:We get rid of parentheses
5x-7x(-1x-7)
We multiply parentheses
7x^2+5x+49x
We add all the numbers together, and all the variables
7x^2+54x
Back to the equation:
-(7x^2+54x)
-5x^2-7x^2-55x-54x=0
We add all the numbers together, and all the variables
-12x^2-109x=0
a = -12; b = -109; c = 0;
Δ = b2-4ac
Δ = -1092-4·(-12)·0
Δ = 11881
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{11881}=109$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-109}{2*-12}=\frac{0}{-24} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+109}{2*-12}=\frac{218}{-24} =-9+1/12 $
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