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2x(x-4)=7x-27
We move all terms to the left:
2x(x-4)-(7x-27)=0
We multiply parentheses
2x^2-8x-(7x-27)=0
We get rid of parentheses
2x^2-8x-7x+27=0
We add all the numbers together, and all the variables
2x^2-15x+27=0
a = 2; b = -15; c = +27;
Δ = b2-4ac
Δ = -152-4·2·27
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*2}=\frac{12}{4} =3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*2}=\frac{18}{4} =4+1/2 $
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