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7x(4x+3)=3x+2
We move all terms to the left:
7x(4x+3)-(3x+2)=0
We multiply parentheses
28x^2+21x-(3x+2)=0
We get rid of parentheses
28x^2+21x-3x-2=0
We add all the numbers together, and all the variables
28x^2+18x-2=0
a = 28; b = 18; c = -2;
Δ = b2-4ac
Δ = 182-4·28·(-2)
Δ = 548
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{137}}{2*28}=\frac{-18-2\sqrt{137}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{137}}{2*28}=\frac{-18+2\sqrt{137}}{56} $
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