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2x(3x+17)=5x+14
We move all terms to the left:
2x(3x+17)-(5x+14)=0
We multiply parentheses
6x^2+34x-(5x+14)=0
We get rid of parentheses
6x^2+34x-5x-14=0
We add all the numbers together, and all the variables
6x^2+29x-14=0
a = 6; b = 29; c = -14;
Δ = b2-4ac
Δ = 292-4·6·(-14)
Δ = 1177
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{-(29)-\sqrt{1177}}{2*6}=\frac{-29-\sqrt{1177}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{1177}}{2*6}=\frac{-29+\sqrt{1177}}{12} $
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