7x(3x-2)=70

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Solution for 7x(3x-2)=70 equation:



7x(3x-2)=70
We move all terms to the left:
7x(3x-2)-(70)=0
We multiply parentheses
21x^2-14x-70=0
a = 21; b = -14; c = -70;
Δ = b2-4ac
Δ = -142-4·21·(-70)
Δ = 6076
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{6076}=\sqrt{196*31}=\sqrt{196}*\sqrt{31}=14\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14\sqrt{31}}{2*21}=\frac{14-14\sqrt{31}}{42} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14\sqrt{31}}{2*21}=\frac{14+14\sqrt{31}}{42} $

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