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5x(5x+7)=6
We move all terms to the left:
5x(5x+7)-(6)=0
We multiply parentheses
25x^2+35x-6=0
a = 25; b = 35; c = -6;
Δ = b2-4ac
Δ = 352-4·25·(-6)
Δ = 1825
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5\sqrt{73}}{2*25}=\frac{-35-5\sqrt{73}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5\sqrt{73}}{2*25}=\frac{-35+5\sqrt{73}}{50} $
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