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4x^2-7x+7x=5x+2
We move all terms to the left:
4x^2-7x+7x-(5x+2)=0
We add all the numbers together, and all the variables
4x^2-(5x+2)=0
We get rid of parentheses
4x^2-5x-2=0
a = 4; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·4·(-2)
Δ = 57
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{-(-5)-\sqrt{57}}{2*4}=\frac{5-\sqrt{57}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*4}=\frac{5+\sqrt{57}}{8} $
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