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5x(3x+38)=90
We move all terms to the left:
5x(3x+38)-(90)=0
We multiply parentheses
15x^2+190x-90=0
a = 15; b = 190; c = -90;
Δ = b2-4ac
Δ = 1902-4·15·(-90)
Δ = 41500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{41500}=\sqrt{100*415}=\sqrt{100}*\sqrt{415}=10\sqrt{415}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-10\sqrt{415}}{2*15}=\frac{-190-10\sqrt{415}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+10\sqrt{415}}{2*15}=\frac{-190+10\sqrt{415}}{30} $
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