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4x(x-2)-3=7x
We move all terms to the left:
4x(x-2)-3-(7x)=0
We add all the numbers together, and all the variables
-7x+4x(x-2)-3=0
We multiply parentheses
4x^2-7x-8x-3=0
We add all the numbers together, and all the variables
4x^2-15x-3=0
a = 4; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·4·(-3)
Δ = 273
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{-(-15)-\sqrt{273}}{2*4}=\frac{15-\sqrt{273}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{273}}{2*4}=\frac{15+\sqrt{273}}{8} $
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