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2x(3x+5)=9.2
We move all terms to the left:
2x(3x+5)-(9.2)=0
We add all the numbers together, and all the variables
2x(3x+5)-9.2=0
We multiply parentheses
6x^2+10x-9.2=0
a = 6; b = 10; c = -9.2;
Δ = b2-4ac
Δ = 102-4·6·(-9.2)
Δ = 320.8
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{-(10)-\sqrt{320.8}}{2*6}=\frac{-10-\sqrt{320.8}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+\sqrt{320.8}}{2*6}=\frac{-10+\sqrt{320.8}}{12} $
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