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6x(4x-3-5x)-5(-7x-3)-3x-1=0
We add all the numbers together, and all the variables
6x(-1x-3)-5(-7x-3)-3x-1=0
We add all the numbers together, and all the variables
-3x+6x(-1x-3)-5(-7x-3)-1=0
We multiply parentheses
-6x^2-3x-18x+35x+15-1=0
We add all the numbers together, and all the variables
-6x^2+14x+14=0
a = -6; b = 14; c = +14;
Δ = b2-4ac
Δ = 142-4·(-6)·14
Δ = 532
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{133}}{2*-6}=\frac{-14-2\sqrt{133}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{133}}{2*-6}=\frac{-14+2\sqrt{133}}{-12} $
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