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7x(x+4)-10=3x+20+4x-2
We move all terms to the left:
7x(x+4)-10-(3x+20+4x-2)=0
We add all the numbers together, and all the variables
7x(x+4)-(7x+18)-10=0
We multiply parentheses
7x^2+28x-(7x+18)-10=0
We get rid of parentheses
7x^2+28x-7x-18-10=0
We add all the numbers together, and all the variables
7x^2+21x-28=0
a = 7; b = 21; c = -28;
Δ = b2-4ac
Δ = 212-4·7·(-28)
Δ = 1225
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{1225}=35$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-35}{2*7}=\frac{-56}{14} =-4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+35}{2*7}=\frac{14}{14} =1 $
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