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4500=10x^2+.75x
We move all terms to the left:
4500-(10x^2+.75x)=0
We get rid of parentheses
-10x^2-.75x+4500=0
We add all the numbers together, and all the variables
-10x^2-0.75x+4500=0
a = -10; b = -0.75; c = +4500;
Δ = b2-4ac
Δ = -0.752-4·(-10)·4500
Δ = 180000.5625
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{-(-0.75)-\sqrt{180000.5625}}{2*-10}=\frac{0.75-\sqrt{180000.5625}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.75)+\sqrt{180000.5625}}{2*-10}=\frac{0.75+\sqrt{180000.5625}}{-20} $
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