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4x^2-9x+20=6x+6
We move all terms to the left:
4x^2-9x+20-(6x+6)=0
We get rid of parentheses
4x^2-9x-6x-6+20=0
We add all the numbers together, and all the variables
4x^2-15x+14=0
a = 4; b = -15; c = +14;
Δ = b2-4ac
Δ = -152-4·4·14
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-1}{2*4}=\frac{14}{8} =1+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+1}{2*4}=\frac{16}{8} =2 $
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