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2x^2+3x+10=4x+32
We move all terms to the left:
2x^2+3x+10-(4x+32)=0
We get rid of parentheses
2x^2+3x-4x-32+10=0
We add all the numbers together, and all the variables
2x^2-1x-22=0
a = 2; b = -1; c = -22;
Δ = b2-4ac
Δ = -12-4·2·(-22)
Δ = 177
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{-(-1)-\sqrt{177}}{2*2}=\frac{1-\sqrt{177}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{177}}{2*2}=\frac{1+\sqrt{177}}{4} $
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