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2x(x-2)=3x+30
We move all terms to the left:
2x(x-2)-(3x+30)=0
We multiply parentheses
2x^2-4x-(3x+30)=0
We get rid of parentheses
2x^2-4x-3x-30=0
We add all the numbers together, and all the variables
2x^2-7x-30=0
a = 2; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·2·(-30)
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*2}=\frac{-10}{4} =-2+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*2}=\frac{24}{4} =6 $
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