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4x^2-7x+4=3x+2
We move all terms to the left:
4x^2-7x+4-(3x+2)=0
We get rid of parentheses
4x^2-7x-3x-2+4=0
We add all the numbers together, and all the variables
4x^2-10x+2=0
a = 4; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·4·2
Δ = 68
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{17}}{2*4}=\frac{10-2\sqrt{17}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{17}}{2*4}=\frac{10+2\sqrt{17}}{8} $
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