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4x^2-5x+7=4x+5
We move all terms to the left:
4x^2-5x+7-(4x+5)=0
We get rid of parentheses
4x^2-5x-4x-5+7=0
We add all the numbers together, and all the variables
4x^2-9x+2=0
a = 4; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·4·2
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*4}=\frac{2}{8} =1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*4}=\frac{16}{8} =2 $
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