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x(4x-27)=7
We move all terms to the left:
x(4x-27)-(7)=0
We multiply parentheses
4x^2-27x-7=0
a = 4; b = -27; c = -7;
Δ = b2-4ac
Δ = -272-4·4·(-7)
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-29}{2*4}=\frac{-2}{8} =-1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+29}{2*4}=\frac{56}{8} =7 $
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