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-4x(2x+7)+3x=12
We move all terms to the left:
-4x(2x+7)+3x-(12)=0
We add all the numbers together, and all the variables
3x-4x(2x+7)-12=0
We multiply parentheses
-8x^2+3x-28x-12=0
We add all the numbers together, and all the variables
-8x^2-25x-12=0
a = -8; b = -25; c = -12;
Δ = b2-4ac
Δ = -252-4·(-8)·(-12)
Δ = 241
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{241}}{2*-8}=\frac{25-\sqrt{241}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{241}}{2*-8}=\frac{25+\sqrt{241}}{-16} $
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