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8-7(4x+1)5x=6-3x
We move all terms to the left:
8-7(4x+1)5x-(6-3x)=0
We add all the numbers together, and all the variables
-7(4x+1)5x-(-3x+6)+8=0
We multiply parentheses
-140x^2-35x-(-3x+6)+8=0
We get rid of parentheses
-140x^2-35x+3x-6+8=0
We add all the numbers together, and all the variables
-140x^2-32x+2=0
a = -140; b = -32; c = +2;
Δ = b2-4ac
Δ = -322-4·(-140)·2
Δ = 2144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2144}=\sqrt{16*134}=\sqrt{16}*\sqrt{134}=4\sqrt{134}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{134}}{2*-140}=\frac{32-4\sqrt{134}}{-280} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{134}}{2*-140}=\frac{32+4\sqrt{134}}{-280} $
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