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7.5x^2+10x=20
We move all terms to the left:
7.5x^2+10x-(20)=0
a = 7.5; b = 10; c = -20;
Δ = b2-4ac
Δ = 102-4·7.5·(-20)
Δ = 700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{7}}{2*7.5}=\frac{-10-10\sqrt{7}}{15} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{7}}{2*7.5}=\frac{-10+10\sqrt{7}}{15} $
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