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2.5x(x+5)=7.5x-0.5
We move all terms to the left:
2.5x(x+5)-(7.5x-0.5)=0
We multiply parentheses
2x^2+10x-(7.5x-0.5)=0
We get rid of parentheses
2x^2+10x-7.5x+0.5=0
We add all the numbers together, and all the variables
2x^2+2.5x+0.5=0
a = 2; b = 2.5; c = +0.5;
Δ = b2-4ac
Δ = 2.52-4·2·0.5
Δ = 2.25
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2.5)-\sqrt{2.25}}{2*2}=\frac{-2.5-\sqrt{2.25}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{2.25}}{2*2}=\frac{-2.5+\sqrt{2.25}}{4} $
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