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3x+1x(7x-12)=2x+5
We move all terms to the left:
3x+1x(7x-12)-(2x+5)=0
We multiply parentheses
7x^2+3x-12x-(2x+5)=0
We get rid of parentheses
7x^2+3x-12x-2x-5=0
We add all the numbers together, and all the variables
7x^2-11x-5=0
a = 7; b = -11; c = -5;
Δ = b2-4ac
Δ = -112-4·7·(-5)
Δ = 261
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{29}}{2*7}=\frac{11-3\sqrt{29}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{29}}{2*7}=\frac{11+3\sqrt{29}}{14} $
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