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5x^2-90=10x+4x^2
We move all terms to the left:
5x^2-90-(10x+4x^2)=0
We get rid of parentheses
5x^2-4x^2-10x-90=0
We add all the numbers together, and all the variables
x^2-10x-90=0
a = 1; b = -10; c = -90;
Δ = b2-4ac
Δ = -102-4·1·(-90)
Δ = 460
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{115}}{2*1}=\frac{10-2\sqrt{115}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{115}}{2*1}=\frac{10+2\sqrt{115}}{2} $
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