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3x+7*7x=3x*8x-1
We move all terms to the left:
3x+7*7x-(3x*8x-1)=0
Wy multiply elements
3x+49x-(3x*8x-1)=0
We get rid of parentheses
3x+49x-3x*8x+1=0
We add all the numbers together, and all the variables
52x-3x*8x+1=0
Wy multiply elements
-24x^2+52x+1=0
a = -24; b = 52; c = +1;
Δ = b2-4ac
Δ = 522-4·(-24)·1
Δ = 2800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-20\sqrt{7}}{2*-24}=\frac{-52-20\sqrt{7}}{-48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+20\sqrt{7}}{2*-24}=\frac{-52+20\sqrt{7}}{-48} $
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