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6(3s-5)7s=25
We move all terms to the left:
6(3s-5)7s-(25)=0
We multiply parentheses
126s^2-210s-25=0
a = 126; b = -210; c = -25;
Δ = b2-4ac
Δ = -2102-4·126·(-25)
Δ = 56700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{56700}=\sqrt{8100*7}=\sqrt{8100}*\sqrt{7}=90\sqrt{7}$$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-90\sqrt{7}}{2*126}=\frac{210-90\sqrt{7}}{252} $$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+90\sqrt{7}}{2*126}=\frac{210+90\sqrt{7}}{252} $
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