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4x^2-12x+16=37/4
We move all terms to the left:
4x^2-12x+16-(37/4)=0
We add all the numbers together, and all the variables
4x^2-12x+16-(+37/4)=0
We get rid of parentheses
4x^2-12x+16-37/4=0
We multiply all the terms by the denominator
4x^2*4-12x*4-37+16*4=0
We add all the numbers together, and all the variables
4x^2*4-12x*4+27=0
Wy multiply elements
16x^2-48x+27=0
a = 16; b = -48; c = +27;
Δ = b2-4ac
Δ = -482-4·16·27
Δ = 576
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{576}=24$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24}{2*16}=\frac{24}{32} =3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24}{2*16}=\frac{72}{32} =2+1/4 $
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