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-12x+2(8x+6)-4x(9-7)=11
We move all terms to the left:
-12x+2(8x+6)-4x(9-7)-(11)=0
We add all the numbers together, and all the variables
-12x+2(8x+6)-4x2-11=0
We add all the numbers together, and all the variables
-4x^2-12x+2(8x+6)-11=0
We multiply parentheses
-4x^2-12x+16x+12-11=0
We add all the numbers together, and all the variables
-4x^2+4x+1=0
a = -4; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-4)·1
Δ = 32
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-4}=\frac{-4-4\sqrt{2}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-4}=\frac{-4+4\sqrt{2}}{-8} $
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