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2+x(5+2x)-7=3x+7
We move all terms to the left:
2+x(5+2x)-7-(3x+7)=0
We add all the numbers together, and all the variables
x(2x+5)-(3x+7)+2-7=0
We add all the numbers together, and all the variables
x(2x+5)-(3x+7)-5=0
We multiply parentheses
2x^2+5x-(3x+7)-5=0
We get rid of parentheses
2x^2+5x-3x-7-5=0
We add all the numbers together, and all the variables
2x^2+2x-12=0
a = 2; b = 2; c = -12;
Δ = b2-4ac
Δ = 22-4·2·(-12)
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*2}=\frac{-12}{4} =-3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*2}=\frac{8}{4} =2 $
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