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7x(x-3)=35(x-3)
We move all terms to the left:
7x(x-3)-(35(x-3))=0
We multiply parentheses
7x^2-21x-(35(x-3))=0
We calculate terms in parentheses: -(35(x-3)), so:We get rid of parentheses
35(x-3)
We multiply parentheses
35x-105
Back to the equation:
-(35x-105)
7x^2-21x-35x+105=0
We add all the numbers together, and all the variables
7x^2-56x+105=0
a = 7; b = -56; c = +105;
Δ = b2-4ac
Δ = -562-4·7·105
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-14}{2*7}=\frac{42}{14} =3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+14}{2*7}=\frac{70}{14} =5 $
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