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30-7x(x-2)=3x+6
We move all terms to the left:
30-7x(x-2)-(3x+6)=0
We multiply parentheses
-7x^2+14x-(3x+6)+30=0
We get rid of parentheses
-7x^2+14x-3x-6+30=0
We add all the numbers together, and all the variables
-7x^2+11x+24=0
a = -7; b = 11; c = +24;
Δ = b2-4ac
Δ = 112-4·(-7)·24
Δ = 793
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{-(11)-\sqrt{793}}{2*-7}=\frac{-11-\sqrt{793}}{-14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{793}}{2*-7}=\frac{-11+\sqrt{793}}{-14} $
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