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4x(x-3)=5x+18
We move all terms to the left:
4x(x-3)-(5x+18)=0
We multiply parentheses
4x^2-12x-(5x+18)=0
We get rid of parentheses
4x^2-12x-5x-18=0
We add all the numbers together, and all the variables
4x^2-17x-18=0
a = 4; b = -17; c = -18;
Δ = b2-4ac
Δ = -172-4·4·(-18)
Δ = 577
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{-(-17)-\sqrt{577}}{2*4}=\frac{17-\sqrt{577}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{577}}{2*4}=\frac{17+\sqrt{577}}{8} $
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