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10x+5=12x(2)+6x
We move all terms to the left:
10x+5-(12x(2)+6x)=0
We add all the numbers together, and all the variables
-(+12x^2+6x)+10x+5=0
We get rid of parentheses
-12x^2-6x+10x+5=0
We add all the numbers together, and all the variables
-12x^2+4x+5=0
a = -12; b = 4; c = +5;
Δ = b2-4ac
Δ = 42-4·(-12)·5
Δ = 256
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{256}=16$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*-12}=\frac{-20}{-24} =5/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*-12}=\frac{12}{-24} =-1/2 $
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