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4x^2-11x+22=6x+7
We move all terms to the left:
4x^2-11x+22-(6x+7)=0
We get rid of parentheses
4x^2-11x-6x-7+22=0
We add all the numbers together, and all the variables
4x^2-17x+15=0
a = 4; b = -17; c = +15;
Δ = b2-4ac
Δ = -172-4·4·15
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7}{2*4}=\frac{10}{8} =1+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7}{2*4}=\frac{24}{8} =3 $
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