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5x^2+15x=35
We move all terms to the left:
5x^2+15x-(35)=0
a = 5; b = 15; c = -35;
Δ = b2-4ac
Δ = 152-4·5·(-35)
Δ = 925
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{37}}{2*5}=\frac{-15-5\sqrt{37}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{37}}{2*5}=\frac{-15+5\sqrt{37}}{10} $
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