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7x(4x-6)+9=7x-5
We move all terms to the left:
7x(4x-6)+9-(7x-5)=0
We multiply parentheses
28x^2-42x-(7x-5)+9=0
We get rid of parentheses
28x^2-42x-7x+5+9=0
We add all the numbers together, and all the variables
28x^2-49x+14=0
a = 28; b = -49; c = +14;
Δ = b2-4ac
Δ = -492-4·28·14
Δ = 833
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-7\sqrt{17}}{2*28}=\frac{49-7\sqrt{17}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+7\sqrt{17}}{2*28}=\frac{49+7\sqrt{17}}{56} $
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