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4x^2+3x-2=25x+100
We move all terms to the left:
4x^2+3x-2-(25x+100)=0
We get rid of parentheses
4x^2+3x-25x-100-2=0
We add all the numbers together, and all the variables
4x^2-22x-102=0
a = 4; b = -22; c = -102;
Δ = b2-4ac
Δ = -222-4·4·(-102)
Δ = 2116
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{2116}=46$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-46}{2*4}=\frac{-24}{8} =-3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+46}{2*4}=\frac{68}{8} =8+1/2 $
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