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(7x+1)(2x-1)=10x+6x+9
We move all terms to the left:
(7x+1)(2x-1)-(10x+6x+9)=0
We add all the numbers together, and all the variables
(7x+1)(2x-1)-(16x+9)=0
We get rid of parentheses
(7x+1)(2x-1)-16x-9=0
We multiply parentheses ..
(+14x^2-7x+2x-1)-16x-9=0
We get rid of parentheses
14x^2-7x+2x-16x-1-9=0
We add all the numbers together, and all the variables
14x^2-21x-10=0
a = 14; b = -21; c = -10;
Δ = b2-4ac
Δ = -212-4·14·(-10)
Δ = 1001
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{1001}}{2*14}=\frac{21-\sqrt{1001}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1001}}{2*14}=\frac{21+\sqrt{1001}}{28} $
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