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(3x+1)(7x-2)=5x+1
We move all terms to the left:
(3x+1)(7x-2)-(5x+1)=0
We get rid of parentheses
(3x+1)(7x-2)-5x-1=0
We multiply parentheses ..
(+21x^2-6x+7x-2)-5x-1=0
We get rid of parentheses
21x^2-6x+7x-5x-2-1=0
We add all the numbers together, and all the variables
21x^2-4x-3=0
a = 21; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·21·(-3)
Δ = 268
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{67}}{2*21}=\frac{4-2\sqrt{67}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{67}}{2*21}=\frac{4+2\sqrt{67}}{42} $
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