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4x^2+75=7x^2
We move all terms to the left:
4x^2+75-(7x^2)=0
We add all the numbers together, and all the variables
-3x^2+75=0
a = -3; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-3)·75
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*-3}=\frac{-30}{-6} =+5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*-3}=\frac{30}{-6} =-5 $
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