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(3.5x)(2x)+x=1076
We move all terms to the left:
(3.5x)(2x)+x-(1076)=0
We add all the numbers together, and all the variables
(+3.5x)2x+x-1076=0
We add all the numbers together, and all the variables
x+(+3.5x)2x-1076=0
We multiply parentheses
6x^2+x-1076=0
a = 6; b = 1; c = -1076;
Δ = b2-4ac
Δ = 12-4·6·(-1076)
Δ = 25825
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25825}=\sqrt{25*1033}=\sqrt{25}*\sqrt{1033}=5\sqrt{1033}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{1033}}{2*6}=\frac{-1-5\sqrt{1033}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{1033}}{2*6}=\frac{-1+5\sqrt{1033}}{12} $
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