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4x^2/0.5625+x2-1.5x=50
We move all terms to the left:
4x^2/0.5625+x2-1.5x-(50)=0
We add all the numbers together, and all the variables
x^2+4x^2/0.5625-1.5x-50=0
We multiply all the terms by the denominator
4x^2+x^2*0.5625-(1.5x)*0.5625-50*0.5625=0
We add all the numbers together, and all the variables
4x^2+x^2*0.5625-(+1.5x)*0.5625-50*0.5625=0
We add all the numbers together, and all the variables
4x^2+x^2*0.5625-(+1.5x)*0.5625-28.125=0
We multiply parentheses
4x^2+x^2*0.5625-0.5625x-28.125=0
Wy multiply elements
4x^2+0.5625x^2-0.5625x-28.125=0
We add all the numbers together, and all the variables
4.5625x^2-0.5625x-28.125=0
a = 4.5625; b = -0.5625; c = -28.125;
Δ = b2-4ac
Δ = -0.56252-4·4.5625·(-28.125)
Δ = 513.59765625
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{-(-0.5625)-\sqrt{513.59765625}}{2*4.5625}=\frac{0.5625-\sqrt{513.59765625}}{9.125} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5625)+\sqrt{513.59765625}}{2*4.5625}=\frac{0.5625+\sqrt{513.59765625}}{9.125} $
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