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2x(5x+3)=14
We move all terms to the left:
2x(5x+3)-(14)=0
We multiply parentheses
10x^2+6x-14=0
a = 10; b = 6; c = -14;
Δ = b2-4ac
Δ = 62-4·10·(-14)
Δ = 596
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{149}}{2*10}=\frac{-6-2\sqrt{149}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{149}}{2*10}=\frac{-6+2\sqrt{149}}{20} $
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