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8x^2=10x+25
We move all terms to the left:
8x^2-(10x+25)=0
We get rid of parentheses
8x^2-10x-25=0
a = 8; b = -10; c = -25;
Δ = b2-4ac
Δ = -102-4·8·(-25)
Δ = 900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{900}=30$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*8}=\frac{-20}{16} =-1+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*8}=\frac{40}{16} =2+1/2 $
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