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6x=(x-5)+4x(5x-6)+3x+4
We move all terms to the left:
6x-((x-5)+4x(5x-6)+3x+4)=0
We calculate terms in parentheses: -((x-5)+4x(5x-6)+3x+4), so:We get rid of parentheses
(x-5)+4x(5x-6)+3x+4
We add all the numbers together, and all the variables
3x+(x-5)+4x(5x-6)+4
We multiply parentheses
20x^2+3x+(x-5)-24x+4
We get rid of parentheses
20x^2+3x+x-24x-5+4
We add all the numbers together, and all the variables
20x^2-20x-1
Back to the equation:
-(20x^2-20x-1)
-20x^2+6x+20x+1=0
We add all the numbers together, and all the variables
-20x^2+26x+1=0
a = -20; b = 26; c = +1;
Δ = b2-4ac
Δ = 262-4·(-20)·1
Δ = 756
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-6\sqrt{21}}{2*-20}=\frac{-26-6\sqrt{21}}{-40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+6\sqrt{21}}{2*-20}=\frac{-26+6\sqrt{21}}{-40} $
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