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2x(2x+7)=x+18
We move all terms to the left:
2x(2x+7)-(x+18)=0
We multiply parentheses
4x^2+14x-(x+18)=0
We get rid of parentheses
4x^2+14x-x-18=0
We add all the numbers together, and all the variables
4x^2+13x-18=0
a = 4; b = 13; c = -18;
Δ = b2-4ac
Δ = 132-4·4·(-18)
Δ = 457
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{-(13)-\sqrt{457}}{2*4}=\frac{-13-\sqrt{457}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{457}}{2*4}=\frac{-13+\sqrt{457}}{8} $
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