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4x^2-5x+18=8x+9
We move all terms to the left:
4x^2-5x+18-(8x+9)=0
We get rid of parentheses
4x^2-5x-8x-9+18=0
We add all the numbers together, and all the variables
4x^2-13x+9=0
a = 4; b = -13; c = +9;
Δ = b2-4ac
Δ = -132-4·4·9
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*4}=\frac{8}{8} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*4}=\frac{18}{8} =2+1/4 $
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