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3x-(5x-3)(2x-4)=-x-4
We move all terms to the left:
3x-(5x-3)(2x-4)-(-x-4)=0
We add all the numbers together, and all the variables
3x-(5x-3)(2x-4)-(-1x-4)=0
We get rid of parentheses
3x-(5x-3)(2x-4)+1x+4=0
We multiply parentheses ..
-(+10x^2-20x-6x+12)+3x+1x+4=0
We add all the numbers together, and all the variables
-(+10x^2-20x-6x+12)+4x+4=0
We get rid of parentheses
-10x^2+20x+6x+4x-12+4=0
We add all the numbers together, and all the variables
-10x^2+30x-8=0
a = -10; b = 30; c = -8;
Δ = b2-4ac
Δ = 302-4·(-10)·(-8)
Δ = 580
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{145}}{2*-10}=\frac{-30-2\sqrt{145}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{145}}{2*-10}=\frac{-30+2\sqrt{145}}{-20} $
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